Efficient computational tools for inverse imaging problems
Lead Research Organisation:
University of Cambridge
Department Name: Applied Maths and Theoretical Physics
Abstract
A photograph taken with current state-of-the-art digital cameras has between 10 to 20 million pixels. Some cameras have up to 41 million sensor pixels. Despite advances in sensor and optical technology, technically perfect photographs are still elusive in demanding conditions. In low light even the best cameras produce noisy images. Casual photographers cannot always hold the camera steady, and the photograph becomes blurry despite advanced shake reduction technologies. We are thus presented with the challenge of improving the photographs in post-processing. This would desirably be an automated process, based on mathematically well understood models that can be relied upon.
The difficulty with real photographs of tens of millions of pixels is that the resulting optimisation problems -- the task of finding the best enhanced image according to a model -- are huge, and computationally very intensive. Moreover, imaging problems generally computationally very intensive. State-of-the-art image processing techniques based on mathematical principles are only up to processing small images in real time. Further, choosing the right parameters for the models can be difficult. Parameter choice can be facilitated, but again in computationally very intensive ways. The question now is, can we design faster optimisation algorithms that would make this and other image processing tasks tractable for real high-resolution photographs?
The objective of the proposed project is to develop optimisation algorithms that are up to this task. The focus of the project is on general methods that will be applicable to a wide variety of image processing tasks and general big data problems. Besides photography, we will apply the developed tools to problems from biology and medicine, involving magnetic resonance imaging and microscopy.
The difficulty with real photographs of tens of millions of pixels is that the resulting optimisation problems -- the task of finding the best enhanced image according to a model -- are huge, and computationally very intensive. Moreover, imaging problems generally computationally very intensive. State-of-the-art image processing techniques based on mathematical principles are only up to processing small images in real time. Further, choosing the right parameters for the models can be difficult. Parameter choice can be facilitated, but again in computationally very intensive ways. The question now is, can we design faster optimisation algorithms that would make this and other image processing tasks tractable for real high-resolution photographs?
The objective of the proposed project is to develop optimisation algorithms that are up to this task. The focus of the project is on general methods that will be applicable to a wide variety of image processing tasks and general big data problems. Besides photography, we will apply the developed tools to problems from biology and medicine, involving magnetic resonance imaging and microscopy.
Planned Impact
Digital images abound in numerous contexts from consumer cameras to professional imaging devices in medicine, earth and planetary sciences, and biology. The resolution of digital images is crucial for their understanding; the better resolved an image is, the more we can say about its contents. In reality, however, noise and sparse acquisition due to technical and physical limitations result in images with low resolution and distortions.
We are thus presented with the challenge of improving these images. Mathematically based higher-order geometric regularisation techniques by far outperform conventional approaches in terms of the visual quality of the results produced. Their efficient computational realisation however still remains poorly understood. In particular, current state-of-the-art techniques are not up to processing in reasonable time ten-million-megapixel photographs or other big images such as diffusion tensor images from medical MRI. In this project, we shall contribute to this understanding by developing novel optimisation methods for the solution of geometrically regularised mathematical imaging models.
The developed image reconstruction models will benefit everyone who deals with digital images. The processing of digital images is growing in importance in many different situations. From the enhancement of digital pictures from our last holidays in Spain to the processing and professional interpretation of images coming from medical imaging tools (e.g., MRI, CT, electron and optical microscopes), from security cameras and satellites, image processing is ubiquitous. Beneficiaries of optimisation methods for image reconstruction developed in this project include medical doctors who use imaging technology to diagnose a patient, the security sector for processing CCTV data, and higher education for making inverse problems, variational methods, and PDEs more accessible through a visual approach.
Moreover, this project will benefit the UK's initiative on Big Data. While our focus is single-disciplinary on mathematical imaging, the developed methods shall contribute to big data optimisation research, and thus benefit a multitude of areas of modern society ranging from sociological studies to economical planning. The ability to handle large amounts of data is one of the key challenges of modern times. Mathematical analysis is at the centre of developing algorithms for understanding big data. An indicator for the importance of algorithms in our society is the letter to the Prime Minister, "THE AGE OF ALGORITHMS", from the Council for Science and Technology (by Sir Mark Walport, and Professor Dame Nancy Rothwell), 7th of June 2013.
We are thus presented with the challenge of improving these images. Mathematically based higher-order geometric regularisation techniques by far outperform conventional approaches in terms of the visual quality of the results produced. Their efficient computational realisation however still remains poorly understood. In particular, current state-of-the-art techniques are not up to processing in reasonable time ten-million-megapixel photographs or other big images such as diffusion tensor images from medical MRI. In this project, we shall contribute to this understanding by developing novel optimisation methods for the solution of geometrically regularised mathematical imaging models.
The developed image reconstruction models will benefit everyone who deals with digital images. The processing of digital images is growing in importance in many different situations. From the enhancement of digital pictures from our last holidays in Spain to the processing and professional interpretation of images coming from medical imaging tools (e.g., MRI, CT, electron and optical microscopes), from security cameras and satellites, image processing is ubiquitous. Beneficiaries of optimisation methods for image reconstruction developed in this project include medical doctors who use imaging technology to diagnose a patient, the security sector for processing CCTV data, and higher education for making inverse problems, variational methods, and PDEs more accessible through a visual approach.
Moreover, this project will benefit the UK's initiative on Big Data. While our focus is single-disciplinary on mathematical imaging, the developed methods shall contribute to big data optimisation research, and thus benefit a multitude of areas of modern society ranging from sociological studies to economical planning. The ability to handle large amounts of data is one of the key challenges of modern times. Mathematical analysis is at the centre of developing algorithms for understanding big data. An indicator for the importance of algorithms in our society is the letter to the Prime Minister, "THE AGE OF ALGORITHMS", from the Council for Science and Technology (by Sir Mark Walport, and Professor Dame Nancy Rothwell), 7th of June 2013.
Organisations
- University of Cambridge (Lead Research Organisation)
- Schlumberger Limited (Collaboration)
- Friedrich-Alexander University Erlangen-Nuremberg (Collaboration)
- University of Manchester (Collaboration)
- University College London (Collaboration)
- Norwegian University of Science and Technology (NTNU) (Collaboration)
- La Trobe University (Collaboration)
- UNIVERSITY OF CAMBRIDGE (Collaboration)
- QUEEN MARY UNIVERSITY OF LONDON (Collaboration)
- Cancer Research UK Cambridge Institute (Collaboration)
- École Polytechnique (Collaboration)
- University of Osnabrück (Collaboration)
- University of Bath (Collaboration)
- University of Lyon (Collaboration)
- GE Healthcare Limited (Collaboration)
- Saarland University (Collaboration)
- Royal Institute of Technology (Collaboration)
- Luebeck University of Applied Sciences (Collaboration)
- King Abdullah University of Science and Technology (KAUST) (Collaboration)
- CLK GmBH (Collaboration)
Publications
Adler J
(2022)
Task adapted reconstruction for inverse problems
in Inverse Problems
Arridge S
(2019)
Solving inverse problems using data-driven models
in Acta Numerica
Arridge S
(2019)
Mini-Workshop: Deep Learning and Inverse Problems
in Oberwolfach Reports
Aviles-Rivero AI
(2022)
GraphXCOVID: Explainable deep graph diffusion pseudo-Labelling for identifying COVID-19 on chest X-rays.
in Pattern recognition
Benning M
(2017)
Scale Space and Variational Methods in Computer Vision
Benning M
(2014)
Phase reconstruction from velocity-encoded MRI measurements--a survey of sparsity-promoting variational approaches.
in Journal of magnetic resonance (San Diego, Calif. : 1997)
Benning M
(2021)
Choose Your Path Wisely: Gradient Descent in a Bregman Distance Framework
in SIAM Journal on Imaging Sciences
Benning M
(2020)
Bregman Itoh-Abe Methods for Sparse Optimisation
in Journal of Mathematical Imaging and Vision
Buet B
(2019)
Partial differential equations and variational methods for geometric processing of images
in The SMAI journal of computational mathematics
Bungert L
(2020)
Variational regularisation for inverse problems with imperfect forward operators and general noise models.
in Inverse problems
Bungert L
(2018)
Blind image fusion for hyperspectral imaging with the directional total variation
in Inverse Problems
Burger M
(2016)
Infimal Convolution Regularisation Functionals of BV and [Formula: see text] Spaces: Part I: The Finite [Formula: see text] Case.
in Journal of mathematical imaging and vision
Burger M
(2018)
Pattern formation of a nonlocal, anisotropic interaction model
in Mathematical Models and Methods in Applied Sciences
Burger M
(2014)
Total variation regularization in measurement and image space for PET reconstruction
in Inverse Problems
Cai X
(2019)
Linkage Between Piecewise Constant Mumford--Shah Model and Rudin--Osher--Fatemi Model and Its Virtue in Image Segmentation
in SIAM Journal on Scientific Computing
Calatroni L
(2016)
Graph Clustering, Variational Image Segmentation Methods and Hough Transform Scale Detection for Object Measurement in Images
in Journal of Mathematical Imaging and Vision
Calatroni L
(2018)
Unveiling the invisible: mathematical methods for restoring and interpreting illuminated manuscripts
in Heritage Science
Calatroni L
(2017)
Infimal Convolution of Data Discrepancies for Mixed Noise Removal
in SIAM Journal on Imaging Sciences
Calatroni Luca
(2016)
New PDE models for imaging problems and applications
Carrillo J
(2021)
Equilibria of an anisotropic nonlocal interaction equation: Analysis and numerics
in Discrete & Continuous Dynamical Systems
| Title | Making stuff disappear using applied mathematics (video) |
| Description | A fun video showing various methods for removing items from a video using applied mathematics |
| Type Of Art | Film/Video/Animation |
| Year Produced | 2019 |
| Impact | This video will reach an international audience through YouTube, engaging researchers, industry and the general public. To date over 1300 people have viewed the video. |
| URL | https://www.youtube.com/watch?v=-yfApxV62hw&feature=youtu.be |
| Description | For automated image analysis and image processing methods sophisticated mathematical methods are needed that can deliver accurate, reliable and efficiently computable results, in particular in the context of large-scale image data as well as nonlinear relations between the measured data and the quantity, e.g. an image of interest we want to retrieve form this data. In this project we have developed novel analysis and reconstruction techniques based on the minimisation of non-smooth energies and the solution of nonlinear and higher-order partial differential equations. These methods are designed for image enhancement, image segmentation, image inpainting, image reconstruction from under sampled indirect measurements (medical imaging, remote sensing), image classification, object tracking and motion estimation, just to name a few. We have contributed to: 1) The development of new models in this regime 2) The mathematical analysis of solutions to these models, providing reconstruction guarantees and qualitative properties of solutions. This is in particular challenging in the context of nonlinear inverse problems (i.e. nonlinear relations between measurements and image information extracted). 3) The efficient and reliable computational solution in the context of large-scale and possible high-dimensional image data. More explicitly we have developed: - A converging computational scheme for depth from focus reconstruction in which the model for computing an depth image from differently focused photographs is a nonlinear one. - An operator splitting approach with convergence guarantees for the solutions of nonlinear inverse imaging problems. - Analysis and computational methods - based on quasi- and semi-smooth Newton schemes - of bilevel learning approaches for image models based on the minimisation of non-smooth energies. - Development of efficient numerical methods for large-scale inverse problems in medical imaging. We developed new algorithms that successfully exploit the problem structure in positron emission tomography (PET) and thereby allow state-of-the-art mathematical modelling to be used in a clinical setting. Moreover, we worked on the mathematical modelling of a-priori knowledge in a multi-modality or multi-channel setting which for instance leads to faster data acquisition for multi-contrast MRI. - We have developed both theory, algorithms and applications for spectral decomposition of nonlinear operators: we have successfully developed a framework to create realistic image fusions of individual images of two faces with a mathematical method called spectral decomposition. We have developed theoretical justifications for the underlying non-linear spectral decomposition and an algorithm that is able to solve this nonlinear problem in a robust and efficient way. - We have been exploring an anisotropic (and hence non-convex) variational model for a structure preserving interpolation of large-scale sparse data (e.g. point cloud data or level lines of a surface that are far apart) with applications in compression for digital elevation maps, point cloud data processing and atomic force microscopy. - We have developed a new video inpainting algorithm called Guidefill, tailored to the unique needs of inpainting as it applies to 3D conversion of high-definition videos, which is the generation of a stereo left and right eye pair of images/videos from a single image/video. Guidefill operates frame by frame for the sake of speed and keeps the user in the loop, with a mechanism to influence the results of inpainting. - We have proposed an anisotropic particle model for the simulation of artificial fingerprints, which are ubiquitous for the development of fingerprint classification methods applied to large databases. - Development of image analysis methods for the analysis of large light microscopy samples of mitotic cells for cancer research. - Development of an efficient numerical method for the segmentation of LiDAR data with a graph clustering approach with applications in forest ecology for the delineation of individual trees in remote sensing data. - We developed stochastic optimisation methods for convex and non-smooth functional minimisation (a typical framework for mathematical imaging problems). These optimisation techniques are heavily used in machine learning problems and turn out to be particularly useful for large-scale and high-dimensional inverse imaging problems, rendering them affordable computationally, even in real-time applications such as clinical imaging. We have also been investigating acceleration strategies in a stochastic optimisation framework. In particular, the highlight of past year's research is extending the local linear convergence study to the stochastic setting, theoretical guaranteed acceleration for FISTA scheme and extending the partial smoothness to the set-valued mapping. - We have proposed a new optimisation approach based on discrete gradients from geometric integration. Our proposal in particular focuses on the case of large-scale non-convex and non-smooth energies and we can show that (under appropriate definitions of stationary points in this context) the sequence produced by our algorithm converges to a stationary point. Moreover, we derive convergence rates for the case of smooth energies. This optimisation technique splits a high-dimensional problem into a large number of one-dimensional problems that can be solved efficiently and in parallel. - We have been working on a Bregman-type optimisation method for solving a very general class of regularised nonlinear inverse problems. - Development of numerical solutions for several bio-mechanical models for motion in intra-cellular fluid flow. These models are typically large-scale and non-convex by nature (based on nonlinearities between the motion and the image sequence) and their numerical treatment therefore challenging. Since in this work we are interested in using numerics for validating these motion models towards microscopy imaging data of these specimen, our numerical ansatz has to be very accurate. Therefore, here we turn to second-order optimisation methods, in particular quasi-Newton solvers that are applied to the derived system of Euler-Lagrange equations. - We have proposed a new type of optimisation methods that are bringing together ideas from structure-preserving integration (a method called discrete gradient approach) together with ideas from large-scale and possibly non-convex optimisation. The advantage of these approaches are that properties of the continuous model can be very naturally preserved in the numerical discretisation; and for the special type of discrete gradient we use that this results in derivative-free optimisation methods. - We have developed new stochastic optimisation approaches for optimising large-scale and non-smooth problems as they typically appear in inverse imaging problems, such as computer tomography. We show in some preliminary examples that these methods are able to render modern mathematical approaches for tomographic image reconstruction computationally feasible for real-time, clinical use. For further development and clinical validation of this idea we will collaborate with medical physics and clinicians in Addenbrookes hospital in the course of an EPSRC funded Healthcare Impact Partnership. |
| Exploitation Route | The results of the project are made available to the scientific community. The dissemination strategies are: 1. They are or will be published in high standard scientific journals, e.g., SIAM Journal on the Imaging Sciences, Mathematical Programming, Journal of Mathematical Imaging and Vision, Inverse Problems, just to name a few. 2. The results are communicated via presentations at the most prestigious international conferences, e.g., SIAM Conference on Imaging Science, Applied Inverse Problems Conference, International Conference on Continuous Optimization. Additionally to publications in mathematical journals, interdisciplinary collaborative efforts spinned off from this research are published in high standard scientific journals in other fields, e.g., of medicine (e.g., Magnetic Resonance in Medicine) and remote sensing (Remote Sensing of Environment). 3. Developed methods and results are provided as preprints and Open Source software on the Cambridge Image Analysis group web page. This guarantees that the developments obtained in this project will be available and have a great impact on the research of optimisation methods and higher-order imaging and their applications on an international level. In particular, all data and associated MATLAB codes are provided on our group website http://www.damtp.cam.ac.uk/research/cia/software/ as well as on repository.cam.ac.uk 4. Some of the outcomes of this project are included in a book I have just published with Cambridge University Press called Partial Differential Equation Methods for Image Inpainting. All the methods are described in detail in this book and open source MATLAB code is provided on MATLAB Central, see http://www.mathworks.com/matlabcentral/fileexchange/34356-higher-order-total-variation-inpainting and http://www.mathworks.com/matlabcentral/fileexchange/55326-four-approaches-to-the-image-inpainting-problem 5. We will be taking the clinical validation of stochastic optimisation for large-scale, non-smooth image reconstruction forward in the course of an EPSRC Healthcare Impact Award (cf. above). |
| Sectors | Aerospace, Defence and Marine,Agriculture, Food and Drink,Digital/Communication/Information Technologies (including Software),Education,Energy,Environment,Healthcare,Manufacturing, including Industrial Biotechology,Culture, Heritage, Museums and Collections,Transport |
| URL | http://www.damtp.cam.ac.uk/research/cia/ |
| Description | 1. We have established a collaboration with NPL which resulted in an NPL-Cambridge CASE PhD Studentship 'Vegetation assessment using machine learning techniques on spectral imaging data' (recently graduated) and NPL funding for a PostDoc for 3 years on "Imaging" which has just ended. Scalable computational techniques arising from the grant have given rise to various new approaches for analysing high-dimensional imaging data, including hyper spectral satellite imaging data and high resolution light-sheet microscopy data. 2. We have established a collaboration with Cantab Capital Partners (a local hedge fund in Cambridge), which has resulted in a 5 million pounds donation to found a new institute in the Mathematics of Information (CCIMI) http://www.ccimi.maths.cam.ac.uk and PhD students in Cambridge working on industrial projects with them. More details on the CCIMI's associated PhD training programme can be found here https://www.maths.cam.ac.uk/postgrad/phd-mathematics-information/cmi 3. We had several new industrial links with Unilever (IAA funded project on the automated analysis and quantification of food microstructure), start up companies such as Iolight with whom we had a summer student working on a project developing image analysis techniques for their portable microscope, see https://iolight.co.uk/iolight-pocket-microscope-fights-drug-resistance-farm-animals/, and several ongoing collaborations with healthcare companies such as Astrazeneca, GSK, Siemens and GE Healthcare, on (among other things, see also our EPSRC funded Maths in Healthcare Hub https://www.cmih.maths.cam.ac.uk ) on multi-modal image reconstruction and analysis for cancer therapies with joint regularisers and variational modelling, fast MR imaging combining motion models with compressed sensing, and stochastic optimisation for PET image reconstruction. 4. Several invites to give interviews and public lectures have arisen from research on the grant - compare engagement section. 5. Collaboration with the Fitzwilliam Museum on virtual arts restoration which has been exhibited in the Colour exhibition in Cambridge http://www.fitzmuseum.cam.ac.uk/colour, and was featured in several public presentations I have given in the last year, the most recent ones in my Gresham lecture 2017 and in a panel discussion on `Unveiling the mysteries of science in art' at the Cambridge Science Festival 2018. See here for more details on the established, Leverhulme funded, research programme https://mach.maths.cam.ac.uk 6. In the course of an EPSRC Healthcare Impact Award we are investigating the clinical use of stochastic optimisation for tomographic image reconstruction. This is a collaboration with the Mathematics Department at the University of Bath, Addenbrookes Hospital and GE Healthcare, see https://petpp.github.io/ 7. Deep neural networks have emerged as interesting computational tools for solving large-scale imaging problems efficiently. This is an exciting research area which promises a step change in large-scale, high resolution imaging. We have made several contributions to this, including stochastic learned iterative approaches for tomographic image reconstruction and plug-and-play methods for inverse problems in imaging more generally. |
| First Year Of Impact | 2015 |
| Sector | Agriculture, Food and Drink,Environment,Healthcare,Culture, Heritage, Museums and Collections |
| Impact Types | Cultural,Societal,Economic |
| Description | PhD student training within the Cantab Capital Institute of the Mathematics of Information |
| Geographic Reach | Multiple continents/international |
| Policy Influence Type | Influenced training of practitioners or researchers |
| URL | http://www.damtp.cam.ac.uk/user/cbs31/MoI/Welcome.html |
| Description | All in one cancer imaging optimisation using an integrated mathematical and deep learning approach |
| Amount | £821,831 (GBP) |
| Organisation | Wellcome Trust |
| Sector | Charity/Non Profit |
| Country | United Kingdom |
| Start | 01/2020 |
| End | 12/2021 |
| Description | CCI Collaborative Fund on Assessing the conservation quality of tropical forest unmanned aerial vehicles |
| Amount | £30,000 (GBP) |
| Organisation | University of Cambridge |
| Department | Cambridge Conservation Initiative |
| Sector | Academic/University |
| Country | United Kingdom |
| Start | 09/2014 |
| End | 09/2016 |
| Description | Cambridge Mathematics of Information in Healthcare (CMIH) |
| Amount | £1,295,778 (GBP) |
| Funding ID | EP/T017961/1 |
| Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
| Sector | Public |
| Country | United Kingdom |
| Start | 08/2020 |
| End | 08/2023 |
| Description | Combining Knowledge And Data Driven Approaches to Inverse Imaging Problems |
| Amount | £1,240,288 (GBP) |
| Funding ID | EP/V029428/1 |
| Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
| Sector | Public |
| Country | United Kingdom |
| Start | 06/2021 |
| End | 05/2026 |
| Description | Donation to build the Cantab Capital Institute for the Mathematics of Information |
| Amount | £5,000,000 (GBP) |
| Organisation | Cantab Capital Partners |
| Sector | Private |
| Country | United Kingdom |
| Start | 11/2015 |
| End | 10/2020 |
| Description | EPSRC Centre for Mathematical and Statistical Analysis of Multimodal Clinical Imaging |
| Amount | £1,923,014 (GBP) |
| Funding ID | EP/N014588/1 |
| Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
| Sector | Public |
| Country | United Kingdom |
| Start | 03/2016 |
| End | 02/2020 |
| Description | EPSRC Healthcare Impact Partnership: PET++: Improving Localisation, Diagnosis and Quantification in Clinical and Medical PET Imaging with Randomised Optimisation |
| Amount | £1,000,000 (GBP) |
| Funding ID | EP/S026045/1 |
| Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
| Sector | Public |
| Country | United Kingdom |
| Start | 09/2019 |
| End | 08/2022 |
| Description | First Grant |
| Amount | £101,000 (GBP) |
| Funding ID | EP/P021298/1 |
| Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
| Sector | Public |
| Country | United Kingdom |
| Start | 05/2017 |
| End | 10/2018 |
| Description | Isaac Newton Institute research programme on Variational methods and effective algorithms for imaging and vision |
| Amount | £80,000 (GBP) |
| Organisation | Isaac Newton Institute for Mathematical Sciences |
| Sector | Academic/University |
| Country | United Kingdom |
| Start | 08/2017 |
| End | 12/2017 |
| Description | Isaac Newton Trust Grant on Automated Contouring for Radiotherapy Treatment Planning |
| Amount | £30,000 (GBP) |
| Organisation | University of Cambridge |
| Department | Isaac Newton Trust |
| Sector | Academic/University |
| Country | United Kingdom |
| Start | 04/2015 |
| End | 12/2015 |
| Description | LMS Undergraduate Research Bursary for Bilevel optimisation for learning the sampling pattern in Magnetic Resonance Tomography |
| Amount | £1,400 (GBP) |
| Organisation | London Mathematical Society |
| Sector | Academic/University |
| Country | United Kingdom |
| Start | 07/2016 |
| End | 09/2016 |
| Description | LMS Undergraduate Research Bursary for Bilevel optimisation for learning the sampling pattern in Magnetic Resonance Tomography, summer 2016 |
| Amount | £1,400 (GBP) |
| Organisation | London Mathematical Society |
| Sector | Academic/University |
| Country | United Kingdom |
| Start | 07/2016 |
| End | 09/2016 |
| Description | Leverhulme Trust Research Grant - Breaking the non-convexity barrier |
| Amount | £250,000 (GBP) |
| Organisation | The Leverhulme Trust |
| Sector | Charity/Non Profit |
| Country | United Kingdom |
| Start | 11/2015 |
| End | 10/2018 |
| Description | MSCA-RISE-2015 - Marie Sklodowska-Curie Research and Innovation Staff Exchange (RISE): CHiPS CHallenges in Preservation of Structure |
| Amount | € 387,000 (EUR) |
| Funding ID | 691070 |
| Organisation | European Commission H2020 |
| Sector | Public |
| Country | Belgium |
| Start | 01/2016 |
| End | 12/2019 |
| Description | MSCA-RISE-2017 - Research and Innovation Staff Exchange: NoMADS: Nonlocal Methods for Arbitrary Data Sources |
| Amount | € 1,111,500 (EUR) |
| Funding ID | 777826 |
| Organisation | European Commission H2020 |
| Sector | Public |
| Country | Belgium |
| Start | 03/2018 |
| End | 02/2022 |
| Description | Mark Foundation Institute for Integrated Cancer Medicine |
| Amount | £8,600,000 (GBP) |
| Organisation | University of Cambridge |
| Department | The Mark Foundation Institute for Integrated Cancer Medicine |
| Sector | Academic/University |
| Country | United Kingdom |
| Start | 07/2018 |
| Description | Mark Foundation Institute for Integrative Cancer Medicine (MI2CM) |
| Amount | £8,600,000 (GBP) |
| Organisation | University of Cambridge |
| Department | The Mark Foundation Institute for Integrated Cancer Medicine |
| Sector | Academic/University |
| Country | United Kingdom |
| Start | 11/2017 |
| End | 10/2020 |
| Description | Mathematical and Statistical Theory of Imaging |
| Amount | £146,400 (GBP) |
| Organisation | University of Cambridge |
| Sector | Academic/University |
| Country | United Kingdom |
| Start | 01/2017 |
| End | 12/2018 |
| Description | NPL postdoctoral fellowship grant for The mathematics of measurement |
| Amount | £250,000 (GBP) |
| Organisation | National Physical Laboratory |
| Sector | Academic/University |
| Country | United Kingdom |
| Start | 04/2018 |
| End | 03/2021 |
| Description | PET++: Improving Localisation, Diagnosis and Quantification in Clinical and Medical PET Imaging with Randomised Optimisation |
| Amount | £821,421 (GBP) |
| Funding ID | EP/S026045/1 |
| Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
| Sector | Public |
| Country | United Kingdom |
| Start | 08/2019 |
| End | 08/2022 |
| Description | Philip Leverhulme Prize - Mathematical and Statistical Sciences 2017 |
| Amount | £100,000 (GBP) |
| Funding ID | https://www.leverhulme.ac.uk/philip-leverhulme-prizes/deep-inversion---towards-adaptive-physical-inversion-models-imaging |
| Organisation | The Leverhulme Trust |
| Sector | Charity/Non Profit |
| Country | United Kingdom |
| Start | 11/2018 |
| End | 10/2020 |
| Description | Postdoctoral Fellowship in The Mathematics of Information |
| Amount | £50,000 (GBP) |
| Organisation | Cognizant Technology Solutions |
| Sector | Private |
| Country | United States |
| Start | 05/2019 |
| End | 04/2020 |
| Description | Predicting Dementia: Optimising and translating AI to improve prognosis and clinical pathways |
| Amount | £764,285 (GBP) |
| Funding ID | 221633/Z/20/Z |
| Organisation | Wellcome Trust |
| Sector | Charity/Non Profit |
| Country | United Kingdom |
| Start | 02/2022 |
| End | 01/2025 |
| Description | Robust and Efficient Analysis Approaches of Remote Imagery for Assessing Population and Forest Health in India |
| Amount | £552,554 (GBP) |
| Funding ID | EP/T003553/1 |
| Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
| Sector | Public |
| Country | United Kingdom |
| Start | 09/2019 |
| End | 09/2021 |
| Description | Turing seed funding for Personalized Breast Cancer Screening |
| Amount | £24,000 (CLF) |
| Organisation | Alan Turing Institute |
| Sector | Academic/University |
| Country | United Kingdom |
| Start | 10/2017 |
| End | 04/2018 |
| Description | Wellcome Trust/ University of Cambridge Senior ISSF internship for the project Development of Image Analysis Algorithms for Monitoring Forest Health from Aircraft |
| Amount | £15,000 (GBP) |
| Organisation | Wellcome Trust |
| Sector | Charity/Non Profit |
| Country | United Kingdom |
| Start | 05/2014 |
| End | 03/2015 |
| Description | rapiD and secuRe AI imaging based diaGnosis, stratification, fOllow-up, and preparedness for coronavirus paNdemics (DRAGON) |
| Amount | € 11,542,642 (EUR) |
| Funding ID | Grant Agreement (GA) No: 101005122 |
| Organisation | European Commission |
| Department | Innovative Medicines Initiative (IMI) |
| Sector | Public |
| Country | Belgium |
| Start | 10/2020 |
| End | 09/2023 |
| Title | Research data supporting "Deep learning as optimal control problems" |
| Description | |
| Type Of Material | Database/Collection of data |
| Year Produced | 2019 |
| Provided To Others? | Yes |
| URL | https://www.repository.cam.ac.uk/handle/1810/296197 |
| Title | Research data supporting 'An Anisotropic Interaction Model for Simulating Fingerprints' |
| Description | This data contains the code and data necessary to reproduce the computational results published in 'An Anisotropic Interaction Model for Simulating Fingerprints'. |
| Type Of Material | Database/Collection of data |
| Year Produced | 2017 |
| Provided To Others? | Yes |
| Title | Research data supporting 'Pattern formation of a nonlocal, anisotropic interaction model' |
| Description | This data contains the code and data necessary to reproduce the computational results published in 'Pattern formation of a nonlocal, anisotropic interaction model'. |
| Type Of Material | Database/Collection of data |
| Year Produced | 2017 |
| Provided To Others? | Yes |
| Title | Research data supporting the publication "Choose your path wisely: gradient descent in a Bregman distance framework" |
| Description | |
| Type Of Material | Database/Collection of data |
| Year Produced | 2020 |
| Provided To Others? | Yes |
| URL | https://www.repository.cam.ac.uk/handle/1810/308472 |
| Title | Research data supporting the publication "Inverse Scale Space Decomposition". |
| Description | This dataset contains MATLAB© code for the numerical computation of the numerical examples described in Section 5.1 and Section 5.2 of the publication "Inverse Scale Space Decomposition". |
| Type Of Material | Database/Collection of data |
| Year Produced | 2017 |
| Provided To Others? | Yes |
| Title | Research data supporting the publication 'Nonlinear Spectral Image Fusion' |
| Description | This is Matlab code for the creation of image fusions based on the nonlinear spectral TV transform. The method of spectral image fusion is explained in the corresponding SSVM publication 'Nonlinear Spectral Image Fusion'. In order to run the automatic image fusion pipeline with the Obama/Reagan example as visualised in the paper, please follow the instructions in the readme.txt file in the folder 'spectralImageFusionOfFaces'. If you want to compute the spectral image fusions of Gauß and Newton in the supplementary files, please follow the instructions in the Matlab live scripts 'gaussnewton.mlx' or 'newtongauss.mlx' in the folder 'Banknote examples'. |
| Type Of Material | Database/Collection of data |
| Year Produced | 2017 |
| Provided To Others? | Yes |
| Description | Anisotropic variational models and PDEs for inverse imaging problems |
| Organisation | Luebeck University of Applied Sciences |
| Country | Germany |
| Sector | Academic/University |
| PI Contribution | In this project, we introduce a new higher-order total directional variation (TDV) regulariser for inverse imaging problems by taking into account the image gradient weighted by the structural content. Theoretical and numerical details are provided for different applications: the reconstruction of noisy images and videos, the image zooming and the interpolation of scattered surface data. The idea of using directional gradients for imaging applications is also used for the generalisation of the osmosis equation, introduced by Weickert and collaborators in 2013, to its anisotropic counter-part. Anisotropic osmosis is applied to the shadow removal problem thus improving upon the isotropic approach by avoiding the blurring artefact due to the isotropic diffusion. The main idea came from CB Schönlieb in Cambridge, and was part of Dr Simone Parisotto's PhD thesis (PhD student in Schönlieb's group). All the research work was done in collaboration with everyone involved. |
| Collaborator Contribution | Equal contribution between: Simon Masnou (Lyon), Jean-Michel Morel (Cachan), Jan Lellmann (Luebeck), Luca Calatroni (Ecole Polytechnique, Paris), and Joachim Weickert (Saarland). |
| Impact | [1] Parisotto S, Lellmann J, Masnou S, Schönlieb C-B. Higher-Order Total Directional Variation. Part I: Imaging Applications. ArXiv e-print (2018) https://arxiv.org/abs/1812.05023 [2] Parisotto S, Masnou S, Schönlieb C-B. Higher-Order Total Directional Variation. Part II: Analysis. ArXiv e-print (2018) https://arxiv.org/abs/1812.05061 [3] Parisotto S, Schönlieb C-B. Total Directional Variation for Video Denoising. ArXiv e-print (2018) https://arxiv.org/abs/1812.05063 [4] Parisotto S, Calatroni L, Caliari M, Schönlieb C-B, Weickert J. Anisotropic osmosis filtering for shadow removal in images. Inverse Problems (2019) https://doi.org/10.1088/1361-6420/ab08d2 |
| Start Year | 2014 |
| Description | Anisotropic variational models and PDEs for inverse imaging problems |
| Organisation | Saarland University |
| Country | Germany |
| Sector | Academic/University |
| PI Contribution | In this project, we introduce a new higher-order total directional variation (TDV) regulariser for inverse imaging problems by taking into account the image gradient weighted by the structural content. Theoretical and numerical details are provided for different applications: the reconstruction of noisy images and videos, the image zooming and the interpolation of scattered surface data. The idea of using directional gradients for imaging applications is also used for the generalisation of the osmosis equation, introduced by Weickert and collaborators in 2013, to its anisotropic counter-part. Anisotropic osmosis is applied to the shadow removal problem thus improving upon the isotropic approach by avoiding the blurring artefact due to the isotropic diffusion. The main idea came from CB Schönlieb in Cambridge, and was part of Dr Simone Parisotto's PhD thesis (PhD student in Schönlieb's group). All the research work was done in collaboration with everyone involved. |
| Collaborator Contribution | Equal contribution between: Simon Masnou (Lyon), Jean-Michel Morel (Cachan), Jan Lellmann (Luebeck), Luca Calatroni (Ecole Polytechnique, Paris), and Joachim Weickert (Saarland). |
| Impact | [1] Parisotto S, Lellmann J, Masnou S, Schönlieb C-B. Higher-Order Total Directional Variation. Part I: Imaging Applications. ArXiv e-print (2018) https://arxiv.org/abs/1812.05023 [2] Parisotto S, Masnou S, Schönlieb C-B. Higher-Order Total Directional Variation. Part II: Analysis. ArXiv e-print (2018) https://arxiv.org/abs/1812.05061 [3] Parisotto S, Schönlieb C-B. Total Directional Variation for Video Denoising. ArXiv e-print (2018) https://arxiv.org/abs/1812.05063 [4] Parisotto S, Calatroni L, Caliari M, Schönlieb C-B, Weickert J. Anisotropic osmosis filtering for shadow removal in images. Inverse Problems (2019) https://doi.org/10.1088/1361-6420/ab08d2 |
| Start Year | 2014 |
| Description | Anisotropic variational models and PDEs for inverse imaging problems |
| Organisation | University of Lyon |
| Country | France |
| Sector | Academic/University |
| PI Contribution | In this project, we introduce a new higher-order total directional variation (TDV) regulariser for inverse imaging problems by taking into account the image gradient weighted by the structural content. Theoretical and numerical details are provided for different applications: the reconstruction of noisy images and videos, the image zooming and the interpolation of scattered surface data. The idea of using directional gradients for imaging applications is also used for the generalisation of the osmosis equation, introduced by Weickert and collaborators in 2013, to its anisotropic counter-part. Anisotropic osmosis is applied to the shadow removal problem thus improving upon the isotropic approach by avoiding the blurring artefact due to the isotropic diffusion. The main idea came from CB Schönlieb in Cambridge, and was part of Dr Simone Parisotto's PhD thesis (PhD student in Schönlieb's group). All the research work was done in collaboration with everyone involved. |
| Collaborator Contribution | Equal contribution between: Simon Masnou (Lyon), Jean-Michel Morel (Cachan), Jan Lellmann (Luebeck), Luca Calatroni (Ecole Polytechnique, Paris), and Joachim Weickert (Saarland). |
| Impact | [1] Parisotto S, Lellmann J, Masnou S, Schönlieb C-B. Higher-Order Total Directional Variation. Part I: Imaging Applications. ArXiv e-print (2018) https://arxiv.org/abs/1812.05023 [2] Parisotto S, Masnou S, Schönlieb C-B. Higher-Order Total Directional Variation. Part II: Analysis. ArXiv e-print (2018) https://arxiv.org/abs/1812.05061 [3] Parisotto S, Schönlieb C-B. Total Directional Variation for Video Denoising. ArXiv e-print (2018) https://arxiv.org/abs/1812.05063 [4] Parisotto S, Calatroni L, Caliari M, Schönlieb C-B, Weickert J. Anisotropic osmosis filtering for shadow removal in images. Inverse Problems (2019) https://doi.org/10.1088/1361-6420/ab08d2 |
| Start Year | 2014 |
| Description | Faster PET Reconstruction by Stochastic Optimisation |
| Organisation | Ecole Polytechnique |
| Country | France |
| Sector | Academic/University |
| PI Contribution | This project is concerned with the efficient reconstruction of positron emission tomography by means of stochastic optimisation. In the last decade, many mathematical tools have been developed that have the ability to enhance clinical imaging in various ways. On the forefront of this wave are non-smooth priors that allow the reconstruction of a smooth image but do not prohibit jumps across meaningful areas like organs in medical imaging. Beside this these new tools also allow the incorporation of a-prior structual knowledge about the solution at hand. However, most of this progress has not been translated into clinical practice as most modern algorithms are too demanding for the huge data sizes encountered. In the past, algorithms have been made "applicable" to clinical practices by only considering a subset if the data at a time. While for some models this leads to satisfactory results, in general this ad-hoc strategy may yield to spurious artefacts. Motivated by the success of similar techniques in machine learning, in this project we extend modern algorithms for imaging that can handle non-smooth priors in a rigorous way to the subset setting by means of "randomisation". While the algorithm and thus its iterates are random, the variances of these are low and converge quickly to the desired deterministic solution. The Cambridge group has contributed to the algorithm development, and the design of the PET++ project (see outputs below). |
| Collaborator Contribution | Matthias Ehrhardt at the University of Bath has lead the algorithm development for stochastic optimisation for PET, and is a co-Lead on the PET++ project. Antonin Chambolle (Ecole Polytechnique) and Peter Richtárik (KAUST) have contributed with their expertise in convex optimisation and subspace decomposition approaches. Pawel Markiewicz (UCL) has contributed with his expertise on PET and associated PET data and reconstruction codes. |
| Impact | [1] Ehrhardt, M. J., Markiewicz, P. J., Schönlieb, C.-B. (2018). Faster PET Reconstruction with Non-Smooth Priors by Randomization and Preconditioning, https://arxiv.org/abs/1808.07150 [2] Ehrhardt, M. J., Markiewicz, P. J., Richtárik, P., Schott, J., Chambolle, A. & Schönlieb, C.-B. (2017). Faster PET Reconstruction with a Stochastic Primal-Dual Hybrid Gradient Method. In Proceedings of SPIE (Vol. 10394, pp. 1-12). San Diego. http://doi.org/10.1117/12.2272946. [3] Chambolle, A., Ehrhardt, M. J., Richtárik, P., & Schönlieb, C.-B. (2017). Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications. to appear in SIAM Journal on Optimization. http://arxiv.org/abs/1706.04957. |
| Start Year | 2016 |
| Description | Faster PET Reconstruction by Stochastic Optimisation |
| Organisation | GE Healthcare Limited |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | This project is concerned with the efficient reconstruction of positron emission tomography by means of stochastic optimisation. In the last decade, many mathematical tools have been developed that have the ability to enhance clinical imaging in various ways. On the forefront of this wave are non-smooth priors that allow the reconstruction of a smooth image but do not prohibit jumps across meaningful areas like organs in medical imaging. Beside this these new tools also allow the incorporation of a-prior structual knowledge about the solution at hand. However, most of this progress has not been translated into clinical practice as most modern algorithms are too demanding for the huge data sizes encountered. In the past, algorithms have been made "applicable" to clinical practices by only considering a subset if the data at a time. While for some models this leads to satisfactory results, in general this ad-hoc strategy may yield to spurious artefacts. Motivated by the success of similar techniques in machine learning, in this project we extend modern algorithms for imaging that can handle non-smooth priors in a rigorous way to the subset setting by means of "randomisation". While the algorithm and thus its iterates are random, the variances of these are low and converge quickly to the desired deterministic solution. The Cambridge group has contributed to the algorithm development, and the design of the PET++ project (see outputs below). |
| Collaborator Contribution | Matthias Ehrhardt at the University of Bath has lead the algorithm development for stochastic optimisation for PET, and is a co-Lead on the PET++ project. Antonin Chambolle (Ecole Polytechnique) and Peter Richtárik (KAUST) have contributed with their expertise in convex optimisation and subspace decomposition approaches. Pawel Markiewicz (UCL) has contributed with his expertise on PET and associated PET data and reconstruction codes. |
| Impact | [1] Ehrhardt, M. J., Markiewicz, P. J., Schönlieb, C.-B. (2018). Faster PET Reconstruction with Non-Smooth Priors by Randomization and Preconditioning, https://arxiv.org/abs/1808.07150 [2] Ehrhardt, M. J., Markiewicz, P. J., Richtárik, P., Schott, J., Chambolle, A. & Schönlieb, C.-B. (2017). Faster PET Reconstruction with a Stochastic Primal-Dual Hybrid Gradient Method. In Proceedings of SPIE (Vol. 10394, pp. 1-12). San Diego. http://doi.org/10.1117/12.2272946. [3] Chambolle, A., Ehrhardt, M. J., Richtárik, P., & Schönlieb, C.-B. (2017). Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications. to appear in SIAM Journal on Optimization. http://arxiv.org/abs/1706.04957. |
| Start Year | 2016 |
| Description | Faster PET Reconstruction by Stochastic Optimisation |
| Organisation | King Abdullah University of Science and Technology (KAUST) |
| Country | Saudi Arabia |
| Sector | Academic/University |
| PI Contribution | This project is concerned with the efficient reconstruction of positron emission tomography by means of stochastic optimisation. In the last decade, many mathematical tools have been developed that have the ability to enhance clinical imaging in various ways. On the forefront of this wave are non-smooth priors that allow the reconstruction of a smooth image but do not prohibit jumps across meaningful areas like organs in medical imaging. Beside this these new tools also allow the incorporation of a-prior structual knowledge about the solution at hand. However, most of this progress has not been translated into clinical practice as most modern algorithms are too demanding for the huge data sizes encountered. In the past, algorithms have been made "applicable" to clinical practices by only considering a subset if the data at a time. While for some models this leads to satisfactory results, in general this ad-hoc strategy may yield to spurious artefacts. Motivated by the success of similar techniques in machine learning, in this project we extend modern algorithms for imaging that can handle non-smooth priors in a rigorous way to the subset setting by means of "randomisation". While the algorithm and thus its iterates are random, the variances of these are low and converge quickly to the desired deterministic solution. The Cambridge group has contributed to the algorithm development, and the design of the PET++ project (see outputs below). |
| Collaborator Contribution | Matthias Ehrhardt at the University of Bath has lead the algorithm development for stochastic optimisation for PET, and is a co-Lead on the PET++ project. Antonin Chambolle (Ecole Polytechnique) and Peter Richtárik (KAUST) have contributed with their expertise in convex optimisation and subspace decomposition approaches. Pawel Markiewicz (UCL) has contributed with his expertise on PET and associated PET data and reconstruction codes. |
| Impact | [1] Ehrhardt, M. J., Markiewicz, P. J., Schönlieb, C.-B. (2018). Faster PET Reconstruction with Non-Smooth Priors by Randomization and Preconditioning, https://arxiv.org/abs/1808.07150 [2] Ehrhardt, M. J., Markiewicz, P. J., Richtárik, P., Schott, J., Chambolle, A. & Schönlieb, C.-B. (2017). Faster PET Reconstruction with a Stochastic Primal-Dual Hybrid Gradient Method. In Proceedings of SPIE (Vol. 10394, pp. 1-12). San Diego. http://doi.org/10.1117/12.2272946. [3] Chambolle, A., Ehrhardt, M. J., Richtárik, P., & Schönlieb, C.-B. (2017). Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications. to appear in SIAM Journal on Optimization. http://arxiv.org/abs/1706.04957. |
| Start Year | 2016 |
| Description | Faster PET Reconstruction by Stochastic Optimisation |
| Organisation | University College London |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | This project is concerned with the efficient reconstruction of positron emission tomography by means of stochastic optimisation. In the last decade, many mathematical tools have been developed that have the ability to enhance clinical imaging in various ways. On the forefront of this wave are non-smooth priors that allow the reconstruction of a smooth image but do not prohibit jumps across meaningful areas like organs in medical imaging. Beside this these new tools also allow the incorporation of a-prior structual knowledge about the solution at hand. However, most of this progress has not been translated into clinical practice as most modern algorithms are too demanding for the huge data sizes encountered. In the past, algorithms have been made "applicable" to clinical practices by only considering a subset if the data at a time. While for some models this leads to satisfactory results, in general this ad-hoc strategy may yield to spurious artefacts. Motivated by the success of similar techniques in machine learning, in this project we extend modern algorithms for imaging that can handle non-smooth priors in a rigorous way to the subset setting by means of "randomisation". While the algorithm and thus its iterates are random, the variances of these are low and converge quickly to the desired deterministic solution. The Cambridge group has contributed to the algorithm development, and the design of the PET++ project (see outputs below). |
| Collaborator Contribution | Matthias Ehrhardt at the University of Bath has lead the algorithm development for stochastic optimisation for PET, and is a co-Lead on the PET++ project. Antonin Chambolle (Ecole Polytechnique) and Peter Richtárik (KAUST) have contributed with their expertise in convex optimisation and subspace decomposition approaches. Pawel Markiewicz (UCL) has contributed with his expertise on PET and associated PET data and reconstruction codes. |
| Impact | [1] Ehrhardt, M. J., Markiewicz, P. J., Schönlieb, C.-B. (2018). Faster PET Reconstruction with Non-Smooth Priors by Randomization and Preconditioning, https://arxiv.org/abs/1808.07150 [2] Ehrhardt, M. J., Markiewicz, P. J., Richtárik, P., Schott, J., Chambolle, A. & Schönlieb, C.-B. (2017). Faster PET Reconstruction with a Stochastic Primal-Dual Hybrid Gradient Method. In Proceedings of SPIE (Vol. 10394, pp. 1-12). San Diego. http://doi.org/10.1117/12.2272946. [3] Chambolle, A., Ehrhardt, M. J., Richtárik, P., & Schönlieb, C.-B. (2017). Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications. to appear in SIAM Journal on Optimization. http://arxiv.org/abs/1706.04957. |
| Start Year | 2016 |
| Description | Faster PET Reconstruction by Stochastic Optimisation |
| Organisation | University of Bath |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | This project is concerned with the efficient reconstruction of positron emission tomography by means of stochastic optimisation. In the last decade, many mathematical tools have been developed that have the ability to enhance clinical imaging in various ways. On the forefront of this wave are non-smooth priors that allow the reconstruction of a smooth image but do not prohibit jumps across meaningful areas like organs in medical imaging. Beside this these new tools also allow the incorporation of a-prior structual knowledge about the solution at hand. However, most of this progress has not been translated into clinical practice as most modern algorithms are too demanding for the huge data sizes encountered. In the past, algorithms have been made "applicable" to clinical practices by only considering a subset if the data at a time. While for some models this leads to satisfactory results, in general this ad-hoc strategy may yield to spurious artefacts. Motivated by the success of similar techniques in machine learning, in this project we extend modern algorithms for imaging that can handle non-smooth priors in a rigorous way to the subset setting by means of "randomisation". While the algorithm and thus its iterates are random, the variances of these are low and converge quickly to the desired deterministic solution. The Cambridge group has contributed to the algorithm development, and the design of the PET++ project (see outputs below). |
| Collaborator Contribution | Matthias Ehrhardt at the University of Bath has lead the algorithm development for stochastic optimisation for PET, and is a co-Lead on the PET++ project. Antonin Chambolle (Ecole Polytechnique) and Peter Richtárik (KAUST) have contributed with their expertise in convex optimisation and subspace decomposition approaches. Pawel Markiewicz (UCL) has contributed with his expertise on PET and associated PET data and reconstruction codes. |
| Impact | [1] Ehrhardt, M. J., Markiewicz, P. J., Schönlieb, C.-B. (2018). Faster PET Reconstruction with Non-Smooth Priors by Randomization and Preconditioning, https://arxiv.org/abs/1808.07150 [2] Ehrhardt, M. J., Markiewicz, P. J., Richtárik, P., Schott, J., Chambolle, A. & Schönlieb, C.-B. (2017). Faster PET Reconstruction with a Stochastic Primal-Dual Hybrid Gradient Method. In Proceedings of SPIE (Vol. 10394, pp. 1-12). San Diego. http://doi.org/10.1117/12.2272946. [3] Chambolle, A., Ehrhardt, M. J., Richtárik, P., & Schönlieb, C.-B. (2017). Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications. to appear in SIAM Journal on Optimization. http://arxiv.org/abs/1706.04957. |
| Start Year | 2016 |
| Description | Flow of Microtubules in the Drosophila Oocyte |
| Organisation | CLK GmBH |
| Country | Germany |
| Sector | Private |
| PI Contribution | The focus of this project is to characterise directionality of plus ends of microtubules in confocal microscopy images of Drosophilia embryos. This goal is particularly challenging due to the high noise level in such data, making it almost impossible to distinguish EB1 fluorescently labelled comets from randomly distributed noise. To overcome this problem, we employ recently developed methods for joint motion estimation and image reconstruction. As a result we are able to estimate motion in image sequences where other state of the art methods fail. My group in Cambridge (in particular my PostDoc Dr Lukas Lang) has contributed the algorithm development for the motion analysis (optical flow). |
| Collaborator Contribution | Our collaborators Isabel Palacios (Queen Mary London) and Mail Drechsler (University of Osnabrück) have contributed with the biological question and the imaging data. Our collaborators Martin Burger (University of Erlangen) and Hendrik Dirks (CLK GmbH) have contributed to initial ideas for the motion estimation algorithm. |
| Impact | M. Drechsler, L. F. Lang, H. Dirks, M. Burger, C.-B. Schönlieb, I. M. Palacios. Optical flow analysis reveals that Kinesin-mediated advection impacts on the orientation of microtubules, submitted, 2019. Preprint: https://www.biorxiv.org/content/10.1101/556043v2 Code: https://zenodo.org/record/2573254#.XIduWS2cZ0s |
| Start Year | 2015 |
| Description | Flow of Microtubules in the Drosophila Oocyte |
| Organisation | Friedrich-Alexander University Erlangen-Nuremberg |
| Country | Germany |
| Sector | Academic/University |
| PI Contribution | The focus of this project is to characterise directionality of plus ends of microtubules in confocal microscopy images of Drosophilia embryos. This goal is particularly challenging due to the high noise level in such data, making it almost impossible to distinguish EB1 fluorescently labelled comets from randomly distributed noise. To overcome this problem, we employ recently developed methods for joint motion estimation and image reconstruction. As a result we are able to estimate motion in image sequences where other state of the art methods fail. My group in Cambridge (in particular my PostDoc Dr Lukas Lang) has contributed the algorithm development for the motion analysis (optical flow). |
| Collaborator Contribution | Our collaborators Isabel Palacios (Queen Mary London) and Mail Drechsler (University of Osnabrück) have contributed with the biological question and the imaging data. Our collaborators Martin Burger (University of Erlangen) and Hendrik Dirks (CLK GmbH) have contributed to initial ideas for the motion estimation algorithm. |
| Impact | M. Drechsler, L. F. Lang, H. Dirks, M. Burger, C.-B. Schönlieb, I. M. Palacios. Optical flow analysis reveals that Kinesin-mediated advection impacts on the orientation of microtubules, submitted, 2019. Preprint: https://www.biorxiv.org/content/10.1101/556043v2 Code: https://zenodo.org/record/2573254#.XIduWS2cZ0s |
| Start Year | 2015 |
| Description | Flow of Microtubules in the Drosophila Oocyte |
| Organisation | Queen Mary University of London |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | The focus of this project is to characterise directionality of plus ends of microtubules in confocal microscopy images of Drosophilia embryos. This goal is particularly challenging due to the high noise level in such data, making it almost impossible to distinguish EB1 fluorescently labelled comets from randomly distributed noise. To overcome this problem, we employ recently developed methods for joint motion estimation and image reconstruction. As a result we are able to estimate motion in image sequences where other state of the art methods fail. My group in Cambridge (in particular my PostDoc Dr Lukas Lang) has contributed the algorithm development for the motion analysis (optical flow). |
| Collaborator Contribution | Our collaborators Isabel Palacios (Queen Mary London) and Mail Drechsler (University of Osnabrück) have contributed with the biological question and the imaging data. Our collaborators Martin Burger (University of Erlangen) and Hendrik Dirks (CLK GmbH) have contributed to initial ideas for the motion estimation algorithm. |
| Impact | M. Drechsler, L. F. Lang, H. Dirks, M. Burger, C.-B. Schönlieb, I. M. Palacios. Optical flow analysis reveals that Kinesin-mediated advection impacts on the orientation of microtubules, submitted, 2019. Preprint: https://www.biorxiv.org/content/10.1101/556043v2 Code: https://zenodo.org/record/2573254#.XIduWS2cZ0s |
| Start Year | 2015 |
| Description | Flow of Microtubules in the Drosophila Oocyte |
| Organisation | University of Osnabrück |
| Country | Germany |
| Sector | Academic/University |
| PI Contribution | The focus of this project is to characterise directionality of plus ends of microtubules in confocal microscopy images of Drosophilia embryos. This goal is particularly challenging due to the high noise level in such data, making it almost impossible to distinguish EB1 fluorescently labelled comets from randomly distributed noise. To overcome this problem, we employ recently developed methods for joint motion estimation and image reconstruction. As a result we are able to estimate motion in image sequences where other state of the art methods fail. My group in Cambridge (in particular my PostDoc Dr Lukas Lang) has contributed the algorithm development for the motion analysis (optical flow). |
| Collaborator Contribution | Our collaborators Isabel Palacios (Queen Mary London) and Mail Drechsler (University of Osnabrück) have contributed with the biological question and the imaging data. Our collaborators Martin Burger (University of Erlangen) and Hendrik Dirks (CLK GmbH) have contributed to initial ideas for the motion estimation algorithm. |
| Impact | M. Drechsler, L. F. Lang, H. Dirks, M. Burger, C.-B. Schönlieb, I. M. Palacios. Optical flow analysis reveals that Kinesin-mediated advection impacts on the orientation of microtubules, submitted, 2019. Preprint: https://www.biorxiv.org/content/10.1101/556043v2 Code: https://zenodo.org/record/2573254#.XIduWS2cZ0s |
| Start Year | 2015 |
| Description | Geometric Integration Methods for Optimisation |
| Organisation | La Trobe University |
| Country | Australia |
| Sector | Academic/University |
| PI Contribution | This project is concerned with the development and analysis of optimisation schemes based on geometric numerical integration methods. Discrete gradient methods are popular numerical schemes for solving systems of ODEs, and are known for preserving structures of the continuous system such as energy dissipation/conservation. Applying discrete gradients to dissipative ODEs/PDEs yields optimisation schemes that preserve the dissipative structure. For example, we consider a derivative-free discrete gradient method for optimising nonsmooth, nonconvex problems in a blackbox setting. This method has been shown to converge to optimal points of the objective function in a general, nonsmooth setting, while retaining favourable properties of gradient flow. This blackbox optimisation framework is useful, for instance, for bilevel optimisation of regularisation parameters in image processing. We (my PostDoc Matthias Ehrhardt and myself) have developed the idea and this topic in Cambridge, and my PhD student Erlend Riis has done all the analysis and numerical tests that are contained in thee papers (see below). |
| Collaborator Contribution | Our collaborator Reinout Quispel (La Trobe, Melbourne, Australia) has contributed expertise in geometric integration. Our collaborator Torbjørn Ringholm (NTNU, Trondheim, Norway) has contributed to the convergence analysis in the smooth case, and was the lead author on the Euler elastica paper. Our collaborator Jasmina Lazic (former MathWorks Cambridge) has contributed to the parallelisation of the discrete gradient method. |
| Impact | E. S. Riis, M. J. Ehrhardt, G. R. W. Quispel, and C.-B. Schönlieb, A geometric integration approach to nonsmooth, nonconvex optimisation, arXiv:1807.07554, 2018. M. Ehrhardt, E. Riis, T. Ringholm, and C.-B. Schönlieb, A geometric integration approach to smooth optimisation: Foundations of the discrete gradient method, arXiv:1805.06444, 2018. T. Ringholm, J. Lazic, C.-B. Schönlieb, Variational image regularization with Euler's elastica using a discrete gradient scheme, SIAM J. Imaging Sci., 11(4), 2665-2691, 2018. Exhibition at MATLAB Expo in Silverstone in 2017. |
| Start Year | 2017 |
| Description | Geometric Integration Methods for Optimisation |
| Organisation | Norwegian University of Science and Technology (NTNU) |
| Country | Norway |
| Sector | Academic/University |
| PI Contribution | This project is concerned with the development and analysis of optimisation schemes based on geometric numerical integration methods. Discrete gradient methods are popular numerical schemes for solving systems of ODEs, and are known for preserving structures of the continuous system such as energy dissipation/conservation. Applying discrete gradients to dissipative ODEs/PDEs yields optimisation schemes that preserve the dissipative structure. For example, we consider a derivative-free discrete gradient method for optimising nonsmooth, nonconvex problems in a blackbox setting. This method has been shown to converge to optimal points of the objective function in a general, nonsmooth setting, while retaining favourable properties of gradient flow. This blackbox optimisation framework is useful, for instance, for bilevel optimisation of regularisation parameters in image processing. We (my PostDoc Matthias Ehrhardt and myself) have developed the idea and this topic in Cambridge, and my PhD student Erlend Riis has done all the analysis and numerical tests that are contained in thee papers (see below). |
| Collaborator Contribution | Our collaborator Reinout Quispel (La Trobe, Melbourne, Australia) has contributed expertise in geometric integration. Our collaborator Torbjørn Ringholm (NTNU, Trondheim, Norway) has contributed to the convergence analysis in the smooth case, and was the lead author on the Euler elastica paper. Our collaborator Jasmina Lazic (former MathWorks Cambridge) has contributed to the parallelisation of the discrete gradient method. |
| Impact | E. S. Riis, M. J. Ehrhardt, G. R. W. Quispel, and C.-B. Schönlieb, A geometric integration approach to nonsmooth, nonconvex optimisation, arXiv:1807.07554, 2018. M. Ehrhardt, E. Riis, T. Ringholm, and C.-B. Schönlieb, A geometric integration approach to smooth optimisation: Foundations of the discrete gradient method, arXiv:1805.06444, 2018. T. Ringholm, J. Lazic, C.-B. Schönlieb, Variational image regularization with Euler's elastica using a discrete gradient scheme, SIAM J. Imaging Sci., 11(4), 2665-2691, 2018. Exhibition at MATLAB Expo in Silverstone in 2017. |
| Start Year | 2017 |
| Description | Integrative Cancer Medicine Collaboration |
| Organisation | Cancer Research UK Cambridge Institute |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | Development of all-in-one cancer imaging pipeline: from raw tomographic measurements to personalised cancer diagnosis and treatment prediction. |
| Collaborator Contribution | Integrative cancer medicine idea; provision of problem and objective; provision of clinical data and expertise. Collaborators: Prof. Evis Sala (Radiology, Cambridge), Prof. Ozan Öktem (KTH, Stockholm), Dr Mireia Crispin-Ortuzar (CRUK CI), Dr Ramona Woitek (Radiology, Cambridge) |
| Impact | Wellcome Trust Application for All-in-one cancer imaging project under the Digital Innovator Award call. Outcome to be known in April 2019. |
| Start Year | 2018 |
| Description | Integrative Cancer Medicine Collaboration |
| Organisation | Royal Institute of Technology |
| Country | Sweden |
| Sector | Academic/University |
| PI Contribution | Development of all-in-one cancer imaging pipeline: from raw tomographic measurements to personalised cancer diagnosis and treatment prediction. |
| Collaborator Contribution | Integrative cancer medicine idea; provision of problem and objective; provision of clinical data and expertise. Collaborators: Prof. Evis Sala (Radiology, Cambridge), Prof. Ozan Öktem (KTH, Stockholm), Dr Mireia Crispin-Ortuzar (CRUK CI), Dr Ramona Woitek (Radiology, Cambridge) |
| Impact | Wellcome Trust Application for All-in-one cancer imaging project under the Digital Innovator Award call. Outcome to be known in April 2019. |
| Start Year | 2018 |
| Description | Mathematical Challenges in Electron Tomography |
| Organisation | University of Manchester |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | Electron microscopy is a powerful tool in the physical, biological, and industrial sciences advancing areas from nanotechnology to drug discovery. Tomography is a mathematical technique used to recover full 3D information from a sequence of 2D images. One of the classical challenges here is to get the best quality reconstruction from the smallest amount of data. Some of our work has been to introduce novel and customised regularisation techniques to address such problems. Recent hardware advances have also extended this to spectral images, where pixel-wise values of the 2D images are vectors rather than greyscale. This data is also very slow to acquire so we need new methods to reconstruct from little and very noisy data. I have a joint PhD student, Mr Robert Tovey, with Paul Midgley in Material Sciences in Cambridge. Together with Rob my group has contributed the development of novel mathematical reconstruction algorithms for electron tomography reconstruction. Our latest project is the derivation of a sound mathematical model and associated numerical algorithm for strain tensor tomography (in collaboration with Bill Lionheart from Manchester). |
| Collaborator Contribution | Our collaborators in the group of Paul Midgley in Cambridge are the problem owners and have contributed with their expert knowledge on electron tomography and associated tomographic imaging data. Our collaborator Bill Lionheart from Manchester has contributed with his expertise on tensor tomography. |
| Impact | Liquid phase blending of metal-organic frameworks L Longley, SM Collins, C Zhou, GJ Smales, SE Norman, NJ Brownbill, ... Nature communications 9 (1), 2135 Entropic comparison of atomic-resolution electron tomography of crystals and amorphous materials SM Collins, RK Leary, PA Midgley, R Tovey, M Benning, CB Schönlieb, ... Physical review letters 119 (16), 166101 Directional sinogram inpainting for limited angle tomography R Tovey, M Benning, C Brune, MJ Lagerwerf, SM Collins, R Leary, ... Inverse Problems Automated Textural Classification of Osteoarthritis Magnetic Resonance Images JD Kaggie, R Tovey, JW MacKay, F Gilbert, FA Gallagher, A McCaskie, ... International Society for Magnetic Resonance in Medicine |
| Start Year | 2017 |
| Description | Sparse regularisation for seismic imaging |
| Organisation | Schlumberger Limited |
| Department | Schlumberger Cambridge Research |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | Ongoing collaboration with Dr Evren Yarman on sparse regularisation and optimisation with applications in seismic imaging. We have co-supervised two summer intern students together in the past and will be collaborating with a visiting student from Ecole Polytechnique in 2017. |
| Collaborator Contribution | Know how and funding. |
| Impact | Joint publication in preparation; joint supervision of mathematics students; industrial talk by Evren Yarman to graduate students in mathematics in Cambridge in February 2017. |
| Start Year | 2015 |
| Description | Unveiling the invisible: mathematical methods for cultural heritage |
| Organisation | University of Cambridge |
| Department | The Fitzwilliam Museum |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | Hypotheses to be tested: In-depth mathematical analysis of imaging data, developed through our collaboration, could transform the ways in which hypotheses in the study of material culture are tested by searching through algorithmically examined data collected by researchers, revealing hidden patterns in paintings, manuscripts and archaeological objects. Project objectives: We will bring cutting-edge mathematical research to the arts and humanities by focusing on three challenging problems: Textural analysis of cross-sections of paint; Virtual restoration of illuminated manuscripts; Classification of Roman pottery. We will also develop an intuitive software package that will make our methodology accessible to a wide range of arts and humanities scholars. My Cambridge group - in particular my PostDocs Dr Kasia Torgonska and Dr Simone Parisotto are developing the mathematical algorithms for all three cultural heritage applications. They will also be the main developers of the modular toolkit. |
| Collaborator Contribution | Dr Launaro (Faculty of Classics, Cambridge) collaborates on the pottery classification part of the project. With his extensive experience in Roman pottery, their excavation, their historical context, their classification and curation, he is key in defining the shape characteristics in pottery (crucial for their automated classification), in formulating the relevant questions in the different stages of the work, and in critically evaluating the results. He is also responsible for steering the shape analysis and classification capabilities of the modular toolkit and making it user-friendly for a wider use by pottery specialists. Dr Spike Bucklow (Hamilton Kerr Institute (HKI), Cambridge) collaborates on the paint cross section classification, the manuscript restoration and provides input to the modular toolkit, helping define user requirements. He provides the conservation and restoration expertise, in particular on the significance of historic pigments, paints and artists' methods etc. for the manuscript restoration and the art historic significance of technical imagery for the paint cross sections. He has curated the existing database of paint cross-section images at HKI, oversees its development in support the automated cross section classification approaches and supervises its use as a test-bed for the modular toolkit. He is driving all the research questions asked of automated analysis in the manuscript restoration, identifying key visual features of interest in digital images of cross-sections and assessing the relevance and efficiency of software-based recognition of those visual features. As specific discriminatory criteria evolve, he advises on their employment, prioritizing sequences of queries and assessing navigation of the data set. He also advises on how the developed clustering techniques for the paint cross section should be integrated in the modular toolkit. Dr Panayotova (Fitzwilliam Museum) provides the expertise on the illuminated manuscripts through her research on over 4000 illuminated manuscripts at the Fitzwilliam Museum and the Cambridge Colleges. At the start of the project, she identified damaged images and prioritised the most important examples in dated and localised manuscripts for mathematical reconstructions. She selects and provides access to c. 200 from the over 35,000 digital images available from manuscripts in the Fitzwilliam Museum and the Colleges, and c. 100 images acquired with multispectral imaging techniques by the Museum's Research Scientist (at no cost to this project). In the course of the project, she also collaborates on the cross section classification, advising on the historical and artistic background of the selected manuscripts, and providing information on the circumstances of the images' original production and subsequent damage. This represents the human-expert knowledge that will be integrated in the automated restoration. She is giving feedback on the art restoration results, advising on the optimal extent of restoration required to maximise the research potential of the original images. Moreover, Dr Panayotova is co-developing the modular-toolkit, in particular influencing its functionality and design. |
| Impact | Calatroni, Luca; Marie d'Autume and, Rob Hocking ; Panayotova, Stella; Parisotto, Simone; Ricciardi, Paola; Schönlieb, Carola-Bibiane Unveiling the invisible: mathematical methods for restoring and interpreting illuminated manuscripts Journal Article In: Heritage Science, 6 (1), pp. 56, 2018. Parisotto, Simone; Calatroni, Luca; Daffara, Claudia Digital Cultural Heritage imaging via osmosis filtering Inproceedings In: Mansouri A. El Moataz A., Nouboud Mammass F D (Ed.): ICISP 2018: Image and Signal Processing, pp. Springer, 2018. Daffara, Claudia; Parisotto, Simone; Ambrosini, Dario A multipurpose, dual-mode imaging in the MWIR range for artwork diagnostic: a systematic approach Journal Article In: Optics and Lasers in Engineering, 2017. Daffara, Claudia; Parisotto, Simone; Mariotti, Paola Ilaria Mid-infrared thermal imaging for an effective mapping of surface materials and sub-surface detachments in mural paintings: integration of thermography and thermal quasi-reflectography Inproceedings In: Optics for Arts, Architecture, and Archaeology, International Society for Optics and Photonics 2015. Leverhulme Trust project on Unveiling the Invisible - 3years from January 2019; GBP 250K. |
| Start Year | 2013 |
| Title | Acceleration of the PDHGM on strongly convex subspaces |
| Description | Citation: Valkonen, T., & Pock, T. (2016). Research data supporting 'Acceleration of the PDHGM on strongly convex subspaces'. [dataset]. https://www.repository.cam.ac.uk/handle/1810/253697 Description: Matlab implementations of algorithms, plus test image and result summaries. This research data supports 'Acceleration of the PDHGM on strongly convex subspaces'. This record will be updated with publication details. Software: Matlab, C, PNG Subjects: Optimisation, primal-dual, image processing Publication Reference: http://arxiv.org/abs/1511.06566 |
| Type Of Technology | Software |
| Year Produced | 2016 |
| Open Source License? | Yes |
| Impact | An accelerated PDHGM code. |
| URL | https://www.repository.cam.ac.uk/handle/1810/253697 |
| Title | An Object-Oriented Matlab-Framework for Inverse Problems (OOMFIP) - Version 0.5 |
| Description | Citation Benning, M. An Object-Oriented Matlab-Framework for Inverse Problems (OOMFIP) - Version 0.5 [dataset]. https://doi.org/10.17863/CAM.281 Description This is an early version of a Matlab toolbox for the easier realisation of first-order splitting methods for the solution of non-smooth variational regularisation methods. Software Matlab (R2014a) Subjects Matlab, inverse problems, first-order methods, regularisation |
| Type Of Technology | Software |
| Year Produced | 2016 |
| Open Source License? | Yes |
| Impact | General framework for optimisation in inverse problems. |
| URL | https://www.repository.cam.ac.uk/handle/1810/256338 |
| Title | An Object-Oriented Matlab-Framework for Inverse Problems (OOMFIP) - Version 0.5 |
| Description | This is an early version of a Matlab toolbox for the easier realisation of first-order splitting methods for the solution of non-smooth variational regularisation methods. |
| Type Of Technology | Software |
| Year Produced | 2016 |
| Open Source License? | Yes |
| Impact | Object-oriented MATLAB framework for solving inverse problems; makes development of new methods within this range much more efficient as it leverages several standard regularisation approaches and their optimisation. |
| URL | https://doi.org/10.17863/CAM.281 |
| Title | Anisotropic osmosis filtering for shadow removal in images |
| Description | We present an anisotropic extension of the isotropic osmosis model that has been introduced by Weickert et al. for visual computing applications, and we adapt it specifically to shadow removal applications. We show that in the integrable setting, linear anisotropic osmosis minimises an energy that involves a suitable quadratic form which models local directional structures. In our shadow removal applications we estimate the local structure via a modified tensor voting approach and use this information within an anisotropic diffusion inpainting that resembles edge-enhancing anisotropic diffusion inpainting. Our numerical scheme combines the nonnegativity preserving stencil of Fehrenbach and Mirebeau with an exact time stepping based on highly accurate polynomial approximations of the matrix exponential. The resulting anisotropic model is tested on several synthetic and natural images corrupted by constant shadows. We show that it outperforms isotropic osmosis, since it does not suffer from blurring artefacts at the shadow boundaries. |
| Type Of Technology | Software |
| Year Produced | 2018 |
| Open Source License? | Yes |
| Impact | Significantly improved shadow removal in digital images; reduces artefacts. |
| URL | https://iopscience.iop.org/article/10.1088/1361-6420/ab08d2 |
| Title | Blind Image Fusion for Hyperspectral Imaging with the Directional Total Variation |
| Description | This code allows to reproduce the results of Blind Image Fusion for Hyperspectral Imaging with the Directional Total Variation |
| Type Of Technology | Software |
| Year Produced | 2017 |
| Open Source License? | Yes |
| Impact | Superresolution of spectral imaging data by using structure from high-res aerial photograph; the same principle can be applied to super resolution in medical imaging (follow on projects related to this are underway). |
| URL | http://iopscience.iop.org/0266-5611/34/4/044003/ |
| Title | Codes supporting 'Block-proximal methods with spatially adapted acceleration' |
| Description | These are Matlab supporting the manuscript `Block-proximal methods with spatially adapted acceleration', available at https://arxiv.org/abs/1609.07373, http://dx.doi.org/10.1553/etna_vol51s15 (Electronic Transactions on Numerical Analysis 51 (2019), 15-49). |
| Type Of Technology | Software |
| Year Produced | 2017 |
| Open Source License? | Yes |
| URL | https://zenodo.org/record/1042418 |
| Title | Codes supporting 'Block-proximal methods with spatially adapted acceleration' |
| Description | These are Matlab supporting the manuscript `Block-proximal methods with spatially adapted acceleration', available at https://arxiv.org/abs/1609.07373, http://dx.doi.org/10.1553/etna_vol51s15 (Electronic Transactions on Numerical Analysis 51 (2019), 15-49). |
| Type Of Technology | Software |
| Year Produced | 2017 |
| Open Source License? | Yes |
| URL | https://zenodo.org/record/1042419 |
| Title | Diffusion tensor imaging with deterministic error bounds |
| Description | Citation: Gorokh, A., Korolev, Y., & Valkonen, T. (2016). Research data supporting "Diffusion tensor imaging with deterministic error bounds" [dataset]. https://www.repository.cam.ac.uk/handle/1810/253422 Description: Source code Software: C, Matlab Publication Reference: https://www.repository.cam.ac.uk/handle/1810/253736 |
| Type Of Technology | Software |
| Year Produced | 2016 |
| Open Source License? | Yes |
| Impact | Software for diffusion tensor imaging |
| URL | https://www.repository.cam.ac.uk/handle/1810/253422 |
| Title | Gradient descent in a generalised Bregman distance framework |
| Description | Research data supporting the paper https://arxiv.org/abs/1612.02506 Martin Benning, Marta M. Betcke, Matthias J. Ehrhardt, Carola-Bibiane Schönlieb "Gradient descent in a generalised Bregman distance framework" [dataset]. https://doi.org/10.17863/CAM.6489 This data contains the corresponding MATLAB©-code for the numerical examples in the conference proceedings paper 'Gradient descent in a generalised Bregman distance framework'. Download the zip-file and extract it to a folder of your choice. Execute the 'setpath.m' file to add all relevant files to the MATLAB© path, and switch to the folder 'Examples'. This folder contains a script named 'phasereconstruction.m' that will compute the numerical examples as presented in the paper. A detailed explanation of the script can be found in terms of the HTML-file 'phasereconstruction.html' in the sub-folder 'Manual'. |
| Type Of Technology | Software |
| Year Produced | 2016 |
| Open Source License? | Yes |
| Impact | Bregman iteration framework for non-convex and non-smooth optimisation. |
| URL | https://www.repository.cam.ac.uk/handle/1810/261315 |
| Title | Learning Filter Functions in Regularisers by Minimising Quotients |
| Description | Learning approaches have recently become very popular in the field of inverse problems. A large variety of methods has been established in recent years, ranging from bi-level learning to high-dimensional machine learning techniques. Most learning approaches, however, only aim at fitting parametrised models to favourable training data whilst ignoring misfit training data completely. In this paper, we follow up on the idea of learning parametrised regularisation functions by quotient minimisation as established in [2]. We extend the model therein to include higher-dimensionalearning filtersl filter functions to be learned and allow for fit- and misfit-training data consisting of multiple functions. We first present results resembling behaviour of well-established derivative-based sparse regularisers like total variation or higher-order total variation in one-dimension. Our second and main contribution is the introduction of novel families of non-derivative-based regularisers. This is accomplished by learning favourable scales and geometric properties while at the same time avoiding unfavourable ones. Reference: [1] Martin Benning, Guy Gilboa, Joana Sarah Grah and Carola-Bibiane Schönlieb. "Learning Filter Functions in Regularisers by Minimising Quotients." Scale Space and Variational Methods in Computer Vision (2017), accepted. [2] Martin Benning, Guy Gilboa, and Carola-Bibiane Schönlieb. "Learning parametrised regularisation functions via quotient minimisation." PAMM 16.1 (2016): 933-936. |
| Type Of Technology | Software |
| Year Produced | 2017 |
| Open Source License? | Yes |
| Impact | Translation of research on learned sparse regularisers to the public |
| URL | https://www.repository.cam.ac.uk/handle/1810/263468 |
| Title | Mathematical Imaging Methods for Mitosis Analysis in Live-Cell Phase Contrast Microscopy |
| Description | We propose a workflow to detect and track mitotic cells in time-lapse microscopy image sequences. In order to avoid the requirement for cell lines expressing fluorescent markers and the associated phototoxicity, phase contrast microscopy is often preferred over fluorescence microscopy in live-cell imaging. However, common specific image characteristics complicate image processing and impede use of standard methods. Nevertheless, automated analysis is desirable due to manual analysis being subjective, biased and extremely time-consuming for large data sets. Here, we present the following workflow based on mathematical imaging methods. In the first step, mitosis detection is performed by means of the circular Hough transform. The obtained circular contour subsequently serves as an initialisation for the tracking algorithm based on variational methods. It is sub-divided into two parts: in order to determine the beginning of the whole mitosis cycle, a backwards tracking procedure is performed. After that, the cell is tracked forwards in time until the end of mitosis. As a result, the average of mitosis duration and ratios of different cell fates (cell death, no division, division into two or more daughter cells) can be measured and statistics on cell morphologies can be obtained. All of the tools are featured in the user-friendly MATLAB® Graphical User Interface MitosisAnalyser. Reference: Joana Sarah Grah, Jennifer Alison Harrington, Siang Boon Koh, Jeremy Andrew Pike, Alexander Schreiner, Martin Burger, Carola-Bibiane Schönlieb, Stefanie Reichelt. "Mathematical imaging methods for mitosis analysis in live-cell phase contrast microscopy." Methods 115 (2017): 91-99. |
| Type Of Technology | Software |
| Year Produced | 2017 |
| Open Source License? | Yes |
| Impact | MitosisAnalyser is a software tool with an easy to use graphical user interface for cancer researchers without prior knowledge on image analysis to use. |
| URL | https://github.com/JoanaGrah/MitosisAnalyser |
| Title | Multi-Contrast MRI Reconstruction with Structure-Guided Total Variation |
| Description | Paper: [SIAM.org][arxiv] Authors: M. Betcke and M. Ehrhardt Abstract: Magnetic resonance imaging (MRI) is a versatile imaging technique that allows different contrasts depending on the acquisition parameters. Many clinical imaging studies acquire MRI data for more than one of these contrasts---such as for instance T1 and T2 weighted images---which makes the overall scanning procedure very time consuming. As all of these images show the same underlying anatomy one can try to omit unnecessary measurements by taking the similarity into account during reconstruction. We will discuss two modifications of total variation---based on i) location and ii) direction---that take structural a priori knowledge into account and reduce to total variation in the degenerate case when no structural knowledge is available. We solve the resulting convex minimization problem with the alternating direction method of multipliers that separates the forward operator from the prior. For both priors the corresponding proximal operator can be implemented as an extension of the fast gradient projection method on the dual problem for total variation. We tested the priors on six data sets that are based on phantoms and real MRI images. In all test cases exploiting the structural information from the other contrast yields better results than separate reconstruction with total variation in terms of standard metrics like peak signal-to-noise ratio and structural similarity index. Furthermore, we found that exploiting the two dimensional directional information results in images with well defined edges, superior to those reconstructed solely using a priori information about the edge location. |
| Type Of Technology | Software |
| Year Produced | 2016 |
| Open Source License? | Yes |
| Impact | Software for joint-reconstruction for multi contrast MRI |
| URL | http://www.damtp.cam.ac.uk/research/cia/software/ |
| Title | Preconditioned ADMM with nonlinear operator constraint |
| Description | Abstract: We are presenting a modification of the well-known Alternating Direction Method of Multipliers (ADMM) algorithm with additional preconditioning that aims at solving convex optimisation problems with nonlinear operator constraints. Connections to the recently developed Nonlinear Primal-Dual Hybrid Gradient Method (NL-PDHGM) are presented, and the algorithm is demonstrated to handle the nonlinear inverse problem of parallel Magnetic Resonance Imaging (MRI). Reference: Martin Benning, Florian Knoll, Carola-Bibiana Schönlieb und Tuomo Valkonen, Preconditioned ADMM with nonlinear operator constraint, IFIP conference proceedings 2015. |
| Type Of Technology | Software |
| Year Produced | 2015 |
| Open Source License? | Yes |
| Impact | Robust method for optimisation for nonlinear inverse problems. |
| URL | https://www.repository.cam.ac.uk/handle/1810/256221 |
| Title | Stochastic PDHG with Arbitrary Sampling and Imaging Applications |
| Description | This package contains an ODL compatible implementation of the Stochastic Primal-Dual Hybrid Gradient algorithm (SPDHG) proposed and analyzed in our associated publication. It is useful to solve inverse problems with non-smooth regularisation and large-scale data. SPDHG is a direct generalization of the popular Primal-Dual Hybrid Gradient algorithm (PDHG) also known as the Chambolle-Pock algorithm. |
| Type Of Technology | Software |
| Year Produced | 2018 |
| Open Source License? | Yes |
| Impact | New EPSRC project on Clinical PET reconstruction. |
| URL | https://epubs.siam.org/doi/10.1137/17M1134834 |
| Description | 21st ECMI Conference on Industrial and Applied Mathematics (ECMI 2021) |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | The series of European Consortium for Mathematics in Industry (ECMI) conferences are devoted to enforcing the interaction between academy and industry, leading to innovations in both fields. These events have attracted leading experts from business, science, and academia, and have promoted the application of novel mathematical technologies to industry. We hope that ECMI 2021 will further enhance multidisciplinary research and development both in academia and industry, leading to the formulation of challenging real-life problems, where mathematics may provide significant new insights and at the same time may be inspired by those interactions. |
| Year(s) Of Engagement Activity | 2021 |
| URL | https://ecmiindmath.org/2020/11/22/21st-ecmi-conference-on-industrial-and-applied-mathematics/ |
| Description | 26th UK Conference on Medical Image Understanding and Analysis |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Postgraduate students |
| Results and Impact | MIUA is a UK-based international conference for the communication of image processing and analysis research and its application to medical imaging and biomedicine. This is a rapidly growing subject with ever increasing real-world applicability. MIUA welcomes all researchers in medical imaging including mathematicians, computer scientists, bioinformaticians, clinicians, engineers and bioscientists. MIUA is the principal UK forum for communicating research progress within the community interested in image analysis applied to medicine and related biological science. The meeting is designed for the dissemination and discussion of research in medical image understanding and analysis, and aims to encourage the growth and raise the profile of this multi-disciplinary field by bringing together the various communities. MIUA covers many topics in medical imaging including: |
| Year(s) Of Engagement Activity | 2022 |
| URL | https://www.miua2022.com/ |
| Description | 91st GAMM Annual Meeting |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | The Annual Meeting of the International Association of Applied Mathematics and Mechanics, the GAMM 2020@21. |
| Year(s) Of Engagement Activity | 2021 |
| URL | https://jahrestagung.gamm-ev.de/jahr2020-2021/annual-meeting/ |
| Description | ATI scoping workshop on Data-Rich Phenomena - Modelling, Analysing and Simulations using Partial Differential Equations |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Other audiences |
| Results and Impact | Background This event was one of a number of scientific scoping workshops funded by the Alan Turing Institute. These workshops have helped to define the research programme at the Alan Turing Institute, whose mission is to undertake data science research at the intersection of computer science, mathematics, statistics and systems engineering. It aims to provide technically informed advice to policy makers and enable researchers from industry and academia to work together towards practical applications and solutions. Partial differential equations (PDE) are equations involving functions and their derivatives - they have applications in the natural and social sciences, engineering, computer science and economics. Today they have found their way into the data sciences, in a variety of ways. PDE models are used directly, for example for data assimilation, image processing, image analysis, shape analysis, inverse problems, computer vision, and modelling complex phenomena such as crowd motion, opinion formation, and option pricing. PDE ideas also serve as an inspiration to formulate and solve data problems on graphs and networks, such as in the use of graph-discretised PDE for various classification and community detection problems, and in the application of Gamma-convergence to link graph and continuum variational classification models (which is crucial for analysing these models and for understanding their scalability). Aims and Objectives This workshop brought together expert mathematicians and statisticians, working on nonlinear, nonlocal, and stochastic PDE models and on large, complex network problems, with industrial and academic data science users. By encouraging discussion among the participants in informal presentations and breakout sessions, it helped identify the most promising research directions combining PDE and data science. Some of the key scientific questions addressed were: Identification of the most promising directions of novel PDE approaches in data science Which data science problems are appropriate for PDE techniques Which numerical PDE based approaches can lead to scalable algorithms that are applicable to very large data sets The use of model based PDE or variational inverse problems for dimension reduction (simplification!) of high dimensional data sets Pinpointing simple, analysable PDE models capable of describing complex data phenomena (e.g. pattern formation, aggregation, transport, drift, diffusion) Using stochastic PDEs to assimilate new data into existing nonlinear or nonlocal models The workshop brought together industrial and academic experts from a diverse set of backgrounds. It explored the potential of PDEs in data science areas, such as data assimilation, data analytics and topological data analysis. This event will be of particular interest to those from the following identified application areas. Healthcare industries including medical, biotechnology Retail/consumer and business analytics Energy and manufacturing Government/public sector Transport Financial Gaming industry |
| Year(s) Of Engagement Activity | 2015 |
| URL | http://www.turing-gateway.cam.ac.uk/drp_dec2015.shtml |
| Description | Alan Turing Institute Workshop on Theoretical and computational approaches to large scale inverse problems |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Other audiences |
| Results and Impact | Inverse problems are at the heart of data science. The field is cross-disciplinary both within mathematics, encompassing aspects of pure, applied as well as statistics, and across subjects, including physical sciences, engineering, medicine and biology to name only a few. Inverse problems arise in almost all fields of science when details of a postulated model have to be determined from a set of observed data. With inverse problems, scientists observe an effect and work to determine the cause; the ultimate goal is to find essential information (an object or material properties) that is hidden within the measurements. Biomedical imaging, for instance, gives rise to a variety of inverse problems in which the common goal is to produce an image visualising the interior of a living organism. Some inversion approaches are based on effective use of a mathematical model in order to make optimal use of the data; other approaches involve modelblind data mining methods. Since inverse problems are concerned with the processing of data and extraction of relevant information, the field is considered part of Information Technology. Inverse problems are mathematically hard, since they are highly nonlinear, illposed and present important challenges of deep mathematical interest which are key to the development of reliable and accurate practical solution methods. Often the observed data is noisy, of large scale and high dimensional, and there is a significant challenge in determining the statistical properties of any proposed inversion. Key scientific question to be answered: ? What methods are practical for large scale inverse problems? ? What sparse representations are useful in practice, and is convex relaxation sufficient for their application in regularisation? ? What posterior estimates are important for uncertainty quantification ? ? How can data science in health care profit from approaches based on computational analysis and statistical inference? ? What probability models can be used in very large dimensional problems where the amount of data is insufficient for robust statistical estimates? ? What is the correct approach to tackling infinitedimensional problems : optimise then discretise, or viceversa? ? How can deterministic and statistical approaches to optimisation be combined ? ? Can Physics inform Data Science ? (ie, what PDEs are useful) ? Can machine learning inform model selection ? ? How can multiple incommensurate data (e.g. in multimodal imaging) be scaled into a single likelihood measure ? Key topics to be addressed: ? Modeling of the physical phenomena, for the forward problem ? Analysis of the corresponding inverse problem ? Identifying appropriate priors from (often large and/or rich) data sets ? Accurate and efficient numerical and statistical treatment of the forward and inverse problems ? Working with scientific computation and visualization aids ? Undertaking experimental verification/model selection ? Providing summary statistics for approximate inference ? Development of appropriate priors for regularisation and Bayesian inference Key sectors involved and impacted: Medical & biomedical, geophysical, computer vision, astrophysics, atmospheric physics, high energy physics, solidstate physics, process engineering, weather forecasting, security screening, nondestructive testing. This workshop is one of a number of scientific scoping workshops will be held, at the British Library and at other locations across the UK by the Alan Turing Institute. These workshops, which were approved via a competitive process, will map out the national and international data science landscape, focussing on areas core to the Institute's mission, including computer science and Iinformatics, the mathematical sciences, social science and ethics. They will also serve as an instrument for the development of a number of coherent research programmes. |
| Year(s) Of Engagement Activity | 2015 |
| URL | http://www.icms.org.uk/workshop.php?id=368 |
| Description | BIRS Women in Inverse Problems |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | The objective of this workshop is to bring together women in the broad and vibrant field of Inverse Problems. Both established as well as early career researchers will come together to discuss their recent research achievements. This workshop will facilitate professional networking and create mentoring opportunities for women researchers. The ultimate goal is to help broaden female participation in research careers in particular in the field of Inverse Problems, as well as to create new research collaborations. |
| Year(s) Of Engagement Activity | 2021 |
| URL | https://www.birs.ca/events/2021/5-day-workshops/21w5035 |
| Description | BIRS Workshop on Optimal Transport meets Probability, Statistics and Machine Learning, 30 April - 5 May 5, 2017, Oaxaca, Mexico. |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | Organizers Guillaume Carlier (Université Paris Dauphine) marco cuturi (ENSAE) Brendan Pass (University of Alberta) Carola-Bibiane Schönlieb (University of Cambridge) Objectives 1) Optimal transport has long standing connections to probability, which have been amplified in recent years. For example, variants of the classical optimal transport problem have arisen in connection to applications in financial mathematics (including transport problems with additional dependence constraints and martingale optimal transport, where versions with several, or even infinitely many, prescribed marginals are also of interest) and Schrödinger's problem of minimizing the relative entropy of stochastic processes with fixed initial and final laws. In addition, Wasserstein barycenters have recently been developed as a natural tool to average or interpolate among several probability measures, against the background geometry of optimal transport. This extends the celebrated notion of displacement interpolation between two measures, and has recently found many fruitful applications, in image processing, economics and statistics. Each of these problems brings forth significant new challenges, both theoretical and computational; in addition to addressing these, we have strong reasons to believe that bringing together leaders in optimal transport with experts in probability might uncover even more connections and will stimulate research on both sides. 2) The interest in multi-marginal optimal transport problems is also rapidly growing, driven in particular by its connection with density functional theory in quantum chemistry and fluid dynamics (Brenier's generalized solutions of incompressibe Euler). Understanding the structure, regularity and sparsity properties of optimal plans for multi-marginal transport problems is a very active and challenging area of research. Fast numerical solvers yet are still to be found to address these typically very high-dimensional problems. One of our goals in gathering specialists of optimal transport (both theoretical and computational), probability and statistics in a broad sense is to better understand how, for instance, Markov Chain Monte Carlo methods could help overcome such a computational bottleneck. 3) As outlined above, OT methods are rapidly developing in statistics and econometrics, one reason-among many others being for instance that the Brenier's map may be viewed as one of the most natural multivariate extensions of the notion of quantile. Statistical inference based on Wasserstein distances is therefore becoming more and more popular. However, there are few rigorous limit theorems (apart from the real line case) which fully justify its use and one aim of this workshop is to make progress on such delicate issues which intimately connect probability, analysis and the geometry of Wasserstein spaces. 4)Representation of datasets, classification and measurement of similarities/disparities between complex data or objects such as images or collection of histograms are ubiquitous problems in machine learning. Optimal transport based distances are used more and more frequently to address these questions. For instance in principal component analysis (PCA) one aims to approximate in the most accurate way a large cloud of points by a small dimensional manifold and geodesic Wasserstein PCA is becoming a popular tool for large collections of histograms. Another important problem is metric learning which can somehow be viewed as a sort of inverse transport problem: what can be infered on the distance between objects given an observed coupling between them? Bringing specialists of questions using optimal transport methods, it is our hope to have a clearer picture and better geometric and analytic understanding on the performances and complexity of computational OT based methods in machine learning. |
| Year(s) Of Engagement Activity | 2017 |
| URL | http://www.birs.ca/events/2017/5-day-workshops/17w5093 |
| Description | CANADIAN APPLIED AND INDUSTRIAL MATHEMATICS SOCIETY 2021 Annual Meeting |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | Each year CAIMS/SCMAI hosts an annual meeting for all members. This meeting is one of the central activities of CAIMS and has been held for over 30 years. The annual meeting covers all areas of applied and industrial mathematics with high profile speakers invited to give keynote addresses on currently active thematic areas. |
| Year(s) Of Engagement Activity | 2021 |
| URL | https://uwaterloo.ca/canadian-applied-industrial-math-society-annual-meeting-2021/ |
| Description | CCIMI New Directions in the Mathematics of Information, Thursday 10th November 2016 |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | Thursday 10th November 2016 Background Launched in May this year, the Cantab Capital Institute for the Mathematics of Information (CCIMI) is now fully operational with research studentships and a number of exciting collaborative projects underway. Established through philanthropic support of £5 million from Cantab Capital Partners, the Institute accommodates research activity on fundamental mathematical problems and methodology for understanding, analysing, processing and simulating data. The data science research performed in the Institute is at the highest international level, with a key aim to extract relevant information from large and high-dimensional data with a predictable certainty. The advance of data science and the solution of big data questions heavily relies on fundamental mathematical techniques and in particular, their intra-disciplinary engagement. This is at the heart of the Institute, involving mathematical expertise ranging from statistics, applied and computational analysis, to topology and discrete geometry - all with the common goal of advancing data science questions. This event provided an opportunity for a more detailed update on current research taking place at the Institute, associated challenges and other potential collaborative opportunities. Aims and Objectives Current research projects being undertaken by the Institute encompass a variety of activity, from the development of mathematical and statistical tools and techniques for high-dimensional data analysis to hybrid image reconstruction and analysis models. As well as the development of rigorous machine learning methodologies that are accessible by mathematical and statistical analysis techniques. Applications of interest include adaptive image analysis, such as image classification, segmentation and enhancement, all the way to inverse problems in industrial and medical imaging. This event provided an update to the original launch in May, providing more detailed information on research projects and collaborations, as well as highlighting potential new ones. It featured presentations of some of the current project collaborations. The Institute currently has 11 projects: Formation and Adaptation of Biological Transportation Networks Statistical and Computational Aspects of Aggregating Data Summaries Mathematics of Machine Learning: Mathematical Learning Methods for Adaptive and Robust Data Analysis Mixing Times Denoising Geodesic Ray Transforms Mathematical challenges in Electron Tomography Mathematical Challenges of Large Environmental Data Sets Computational and Statistical Joint Image Analysis Statistical Applications of Persistent Homology Bayesian Inference for Discretely Sampled Diffusions - Solving the Nonlinear Inverse Problem To Create a Semantic Search Engine for Mathematical Literature For more information on these projects please visit the CCIMI Website. The Institute's research and projects cover a diverse range of areas across Big Data and so we expect this event to be of interest to individuals from multiple researcher, industry and public communities. Presentations were followed by a drinks and networking reception and the afternoon finished with a Public Lecture by David Spiegelhalter. A copy of the programme can be found here. |
| Year(s) Of Engagement Activity | 2016 |
| URL | http://www.turing-gateway.cam.ac.uk/event/tgmw38 |
| Description | Cantab Capital Institute for the Mathematics of Information -- Launch Event, 9 May 2016, Isaac Newton Institute, Cambridge, UK. |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | This event celebrated the launch of an exciting new research Institute which is a collaboration between the Cantab Capital Partners LLP and the University of Cambridge. Hosted within the Faculty of Mathematics of the University of Cambridge, the Cantab Capital Institute for the Mathematics of Information will push the boundaries of information science. Established through philanthropic support of £5 million from Cantab Capital Partners, the Institute will accommodate research activity on fundamental mathematical problems and methodology for understanding, analysing, processing and simulating data. Data science research performed in the Institute will be on the highest international level, aiming to extract the relevant information from large-and high-dimensional data with a predictable certainty. At the heart of the Institute, will be the fundamental mathematical techniques and their intra-disciplinary engagement, upon which, the solution of big data questions so heavily relies. This is crucial in order to ensure advancements in data science. Aims and Objectives This launch event provided an opportunity to learn more about the work of the Institute, such as the specific questions that feed into fundamental methodology development. It is anticipated that the research will focus on various applications across a number of interdisciplinary engagements. These could include for instance, economists and social scientists on questions about financial markets and the internet, or with physicists and engineers on software and hardware development questions in the context of security. Presentations at the event introduced areas of mathematical expertise represented in the Institute and outline how fundamental techniques can be drawn on to meet the challenge of deciphering meaning in the ever growing volumes of data. Academic expertise at the Institute includes: Statistics Applied and Computational Analysis Stochastic Analysis and Probability Inverse Problems Convex Analysis Stochastic and Sparse Optimisation Compressed Sensing and Sampling Theory Partial Differential Equations Number Theory Quantum Computing, Cryptography and Communication The highlight of the launch was the inaugural lecture of the Institute given by Professor Ronald DeVore from Texas A&M University. Ron is one of the key figures of modern applied mathematics and made substantial contributions to approximation theory, numerical analysis of partial differential equations, wavelet transforms, machine learning algorithms and the theory of compressive sensing. |
| Year(s) Of Engagement Activity | 2016 |
| URL | http://www.turing-gateway.cam.ac.uk/event/tgmw34 |
| Description | Celebrating Chris Budd: A leader in mathematical innovation turns 60 |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | On the 4th of March 2020 we came together at the University of Bath and celebrate the 60th birthday of our colleague, friend and collaborator Chris Budd. The aim of this workshop was to bring together collaborators, former PhD students and PostDocs of Chris to celebrate him and his achievements in mathematical innovation over his long and fruitful academic career. |
| Year(s) Of Engagement Activity | 2019 |
| URL | https://sites.google.com/view/chrisbudd60/home |
| Description | Computational Mathematics and Machine Learning |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | The aim of this workshop is to formulate a plan for future developments within the area of computational science and engineering (CSE) making use of machine learning techniques. We will discuss the impact that machine learning has already made or will make on computational mathematics, and how the ideas from computational mathematics, particularly numerical analysis, can be used to help understanding and better formulating machine learning models. In the annex, the state of the art is provided in more detail. The question is: which research directions are most promising? What should we concentrate on? How can we combine physics-based and data-based techniques? Can we formulate joint projects? Or maybe a joint organisation for the discussion and dissemination of new developments? In this workshop, we will address the following two very important questions: (1) How machine learning has already impacted and will further impact computational mathematics, scienti?c computing and computational science? (2) How computational mathematics, particularly numerical analysis, can impact machine learning? To accomplish the aforementioned aim, in this workshop, we review what has been learned on these two issues. We will discuss some of the most important progress that has been made on the foregoing two issues, and where new developments should take place. This workshop will be considered a success if we have been able to put things into a perspective that will help to integrate machine learning with computational mathematics, and produced (at the end of the workshop) a sound plan for future research directions in several of the areas mentioned in Section 4. We will identify the most promising research directions, networking activities, as well as building of new collaborations between participants. |
| Year(s) Of Engagement Activity | 2021 |
| URL | https://www.lorentzcenter.nl/computational-mathematics-and-machine-learning.html |
| Description | Deep Learning and Inverse Problems (NeurIPS Workshop) |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | This virtual workshop aims at bringing together theoreticians and practitioners in order to chart out recent advances and discuss new directions in deep learning-based approaches for solving inverse problems in the imaging sciences and beyond. |
| Year(s) Of Engagement Activity | 2021 |
| URL | https://deep-inverse.org/index.html |
| Description | Eighth International Conference on Scale Space and Variational Methods in Computer Vision (SSVM) |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | SSVM is a biannual meeting within the area of Computer Vision and Image Analysis. SSVM focuses especially on multiscale analysis of image content, partial differential equations, geometric and level-set methods, variational methods, and optimization. |
| Year(s) Of Engagement Activity | 2021 |
| URL | https://ssvm2021.sciencesconf.org/ |
| Description | General meeting of the European Women in Mathematics Association, 3-7 September 2018, Graz, Austria. Co-organisers: K. Baur, K. Hess, E. Resmerita and S. Terracini. |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Postgraduate students |
| Results and Impact | General Meeting of the European Women in Mathematics Association |
| Year(s) Of Engagement Activity | 2018 |
| URL | https://sites.google.com/site/ewmgm18/ |
| Description | IEEE International Symposium on Biomedical Imaging |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | The IEEE International Symposium on Biomedical Imaging (ISBI) is a scientific conference dedicated to mathematical, algorithmic, and computational aspects of biological and biomedical imaging, across all scales of observation. It fosters knowledge transfer among different imaging communities and contributes to an integrative approach to biomedical imaging. |
| Year(s) Of Engagement Activity | 2021 |
| URL | https://biomedicalimaging.org/2021/ |
| Description | IMA Conference on Inverse Problems |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | Tuesday 19th - Thursday 21st September 2017 An inverse problem denotes the task of computing an unknown physical quantity from indirect measurements. The corresponding forward problem maps the physical quantity to the measurements. In most realistic situations the solution of the inverse problem is challenging, complicated by incomplete and noisy measurements, as well as non-invertible forward operators which render the inverse problem ill-posed (that is lack of stability and/or uniqueness of solutions). Inverse problems appear in many practical applications in biology, medicine, weather forecasting, chemistry, engineering, physics, to name but a few, and their analysis and solution presents considerable challenges in mathematics and statistics. This conference will bring together mathematicians and statisticians, working on theoretical and numerical aspects of inverse problems, and engineers, physicists and other scientists, working on challenging inverse problem applications. We welcome industrial representatives, doctoral students, early career and established academics working in this field to attend. Conference topics: Imaging Regularisation theory Statistical inverse problems Sampling Data assimilation Inverse problem applications Confirmed Invited Speakers: Dr Marta M. Betcke (University College London) Professor Dan Crisan (Imperial College London) Professor Jari Kaipio (University of Auckland, New Zealand) Professor Dirk Lorenz (TU Braunschweig, Germany) Professor Bill Symes (Rice University) Dr Tanja Tarvainen (University of Eastern Finland) Organising Committee: Carola-Bibiane Schönlieb (Cambridge University) - Chair Cristiana Sebu (Oxford Brookes) - Co-chair Paul Ledger (Swansea University) Bill Lionheart (University of Manchester) Scientific Committee: Simon Arridge (University College London) Martin Burger (University of Münster) Daniela Calvetti (Case Western Reserve University) Paul Childs Barbara Kaltenbacher (University of Klagenfurt) Roland Potthast (University of Reading) Samuli Siltanen (University of Helsinki) |
| Year(s) Of Engagement Activity | 2017 |
| URL | http://www.ima.org.uk/conferences/conferences_calendar/inverse-problems.html |
| Description | IMA Conference on Inverse Problems: From Theory To Application |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | This conference brought together mathematicians and statisticians, working on theoretical and numerical aspects of inverse problems, as well as engineers, physicists, and other scientists, working on challenging inverse problem applications. We welcomed industrial representatives, doctoral students, early career and established academics working in this field to attend. |
| Year(s) Of Engagement Activity | 2019 |
| URL | https://ima.org.uk/11329/2nd-ima-conference-on-inverse-problems-from-theory-to-application/ |
| Description | IMAGES network |
| Form Of Engagement Activity | Engagement focused website, blog or social media channel |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Other audiences |
| Results and Impact | Cambridge is home to a wealth of scientific research which includes developing tools for acquisition, visualization, processing and analysis of images. Mathematicians and engineers create image-processing and analysis algorithms, e.g. image reconstruction, image de-noising and restoration algorithms, methods for object segmentation and tracking, in particular in the presence of large-scale imaging data. At the MRRC, fluid-gas dynamics and chemical reactions are investigated using Magnetic Resonance Tomographic Imaging (MRI) as a visualisation and quantification technique. At the Cancer Research UK Cambridge Institute, light microscopy and medical imaging are exciting research fields. A collaboration between microscopists and mathematicians e.g. leads to new ways of tracking and analyzing the effect of cancer drugs during mitosis. At the FM/HKI spectroscopy methods underpin the non-invasive analyses of materials and techniques, conservation and cross-disciplinary interpretation of paintings, illuminated manuscripts and Egyptian papyri. The complex process, from acquiring images to their interpretation and problem-solving applications, requires multi-expertise partnerships. Different problems and image applications inform similar methodologies and interpretative strategies. Cross-disciplinary collaboration is needed to analyze the image-information not explicit in machine-generated data. For instance, in Magnetic Resonance Tomography, Positron Emission Tomography, microscopy imaging or seismic imaging, the combined expertise of mathematicians, engineers, computer scientists, medical doctors and geophysicists turns samples of Fourier-, Radon-transform data or electromagnetic waves into meaningful images of the brain, heart activity or ozone density in the atmosphere. Analyses of artist's materials and techniques, on the other hand, unite chemists, physicists, mathematicians, biologists, imaging scientists, conservators, artists and intellectual historians. We aim to stimulate new inquiries and focused dialogues between the sciences, arts and humanities by providing them with a platform for communication. |
| Year(s) Of Engagement Activity | 2014,2015,2016 |
| URL | http://www.images.group.cam.ac.uk |
| Description | INTERACT 2021 "Sense, Feel, Design" |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | The theme of INTERACT 2021 "Sense, Feel, Design" highlights the new challenges of interaction design. Technology is today more and more widespread, pervasive and blended in the world we live in. On one side, devices that sense humans' activities have the potential to provide an enriched interaction. On the other side, the user experience can be further enhanced by exploiting multisensorial technologies. Not only the traditional human senses of vision and hearing, but also senses of touch, smell, and taste, as well as emotions are to be taken into account when designing for future interactions. INTERACT 2021 represents the right venue to debate such new challenges. Another hot topic of this edition is Human-AI Interaction, focusing on the design of human-centered intelligent systems. |
| Year(s) Of Engagement Activity | 2021 |
| URL | https://www.interact2021.org/ |
| Description | LMS meetings on Current frontiers in inverse problems: from theory to applications |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Other audiences |
| Results and Impact | In 1976 Keller formulated the following very general definition of inverse problems, which is often cited in the literature: "We call two problems inverses of one another if the formulation of each involves all or part of the solution of the other. Often, for historical reasons, one of the two problems has been studied extensively for some time, while the other is newer and not so well understood. In such cases, the former problem is called the direct problem, while the latter is called the inverse problem." Inverse problems appear in many situations in physics, engineering, biology and medicine. The main mathematical problem is the well (ill) - posedness of the inversion process. Indeed, in practice most inverse problems are ill-posed in terms of non-uniqueness or lack of stability of the inversion. We hold four LMS meetings on inverse problems every year that bring together researchers who work on advancing the field of inverse problems, both from a theoretical and from an applied point of view. |
| Year(s) Of Engagement Activity | 2014,2015,2016 |
| URL | http://www.damtp.cam.ac.uk/user/cbs31/LMS_Inverse_Day_Edinburgh/Home.html |
| Description | MFO mini-workshop on Deep Learning and Inverse Problems, 4-10 March 2018, Oberwolfach, Germany. Co-organisers: S. Arridge, M. de Hoop and P. Maass. |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Other audiences |
| Results and Impact | Oberwolfach Workshop on Inverse Problems and deep learning. |
| Year(s) Of Engagement Activity | 2018 |
| URL | https://www.mfo.de/occasion/1810c/www_view |
| Description | Mathematics of deep learning |
| Form Of Engagement Activity | A formal working group, expert panel or dialogue |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | Aiming to derive a mathematical foundation of deep learning, this programme addresses theoretical questions in two realms: (1) Theoretical foundations of deep learning independent of a particular application. (2) Theoretical analysis of the potential and the limitations of deep learning for mathematical methodologies, in particular, for inverse problems and partial differential equations. The main goal of this programme is to achieve substantial progress in developing a theoretical foundation of deep learning. For this, the programme will for the first time gather the top experts from various areas of mathematics and of the theory of machine learning, including computer scientists, physicists, and statisticians in one place, initiating collaborations across intra- and interdisciplinary boundaries and thereby generating unprecedented research dynamics. |
| Year(s) Of Engagement Activity | 2021 |
| URL | https://www.newton.ac.uk/event/mdl/ |
| Description | Mathematisches Forschungsinstitut Oberwolfach - Geometric Numerical Integration |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | The topics of the workshop included interactions between geometric numerical integration and numerical partial differential equations; geometric aspects of stochastic differential equations; interaction with optimisation and machine learning; new applications of geometric integration in physics; problems of discrete geometry, integrability, and algebraic aspects. |
| Year(s) Of Engagement Activity | 2021 |
| URL | https://publications.mfo.de/handle/mfo/3860 |
| Description | Mathematisches Forschungsinstitut Oberwolfach - Mini-Workshop: Deep Learning and Inverse Problems |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | Machine learning and in particular deep learning offer several data-driven methods to amend the typical shortcomings of purely analytical approaches. The mathematical research on these combined models is presently exploding on the experimental side but still lacking on the theoretical point of view. This workshop addresses the challenge of developing a solid mathematical theory for analyzing deep neural networks for inverse problems. |
| Year(s) Of Engagement Activity | 2021 |
| URL | https://publications.mfo.de/handle/mfo/3633 |
| Description | Model-based learning in imaging |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | SIAM's Annual Meeting provides a broad view of the state of the art in applied mathematics, computational science, and their applications through invited presentation, prize lectures, minisymposia, contributed papers and posters. |
| Year(s) Of Engagement Activity | 2017 |
| URL | https://archive.siam.org/meetings/an17/ |
| Description | PLUS article What the eye can't see |
| Form Of Engagement Activity | A magazine, newsletter or online publication |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Public/other audiences |
| Results and Impact | Pictures play a vital role in our lives. They allow us to discover the world, to understand it and to enjoy it. Our own pair of eyes is a powerful tool, but modern imaging technology goes a lot further, revealing distant galaxies and tiny cells in our bodies. Mathematics is the language that underlies this technology, which is why the Cambridge Image Analysis Group, led by Carola-Bibiane Schönlieb, is at home in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge. |
| Year(s) Of Engagement Activity | 2016 |
| URL | https://plus.maths.org/content/what-eye-cant-see |
| Description | PLUS magazine Mathematical Moments |
| Form Of Engagement Activity | A press release, press conference or response to a media enquiry/interview |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Public/other audiences |
| Results and Impact | Mathematical moments: Carola-Bibiane Schönlieb Carola-Bibiane Schönlieb has a fascinating job: she works on the mathematics behind image analysis. It finds application in all sorts of areas, from medical imaging, such as MRI scans, to forest ecology, which sees scientists trying to gain information about forests from pictures taken from the air. In this brief interview Carola tells us why she likes doing maths, recalls some of her favourite mathematical moments, and explains why creativity is essential in mathematics. |
| Year(s) Of Engagement Activity | 2016 |
| URL | https://plus.maths.org/content/mathematical-moments-carola-schonlieb |
| Description | POEMS workshop on Big Data, Multimodality & Dynamic Models in Biomedical Imaging, 9th March 2016, Isaac Newton Institute, Cambridge, UK |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | Wednesday 9th March 2016 Background We are currently experiencing many new exciting developments in imaging technology in biology and medicine. New advances in tomographic imaging, such as photoacoustic tomography, electron tomography, multicontrast magnetic resonance tomography (MRT) and combined MR with positron emission tomography (PET), as well as new technology in microscopy such as lightsheet microscopy, only mark the beginning of an era which revolutionises the extent of what we can see. New imaging technology always goes side by side with the need of mathematical models to maximise the information gain from these novel imaging techniques. For instance, previously tomographic imaging and light microscopy were separate imaging modalities, which were difficult to cross correlate. However, rapid development of new imaging hardware (light sheet, polarized PET, MRI), is now opening up new avenues for translational multimodal imaging. These developments are supported by sophisticated and rigorous mathematical models, which enhance the information in one imaging modality with information from another. Aims and Objectives New imaging technologies however, also bring new challenges to be overcome. In electron tomography for example, the limited angle problem is an intrinsic hardware limitation which results in viewpoint angles in which the imaged specimen cannot be resolved. Dynamic imaging techniques produce huge amounts of image data which require reliable and efficient methods for interpretation and analysis. This one day meeting aimed to bring together those working on advances in imaging technology with researchers who investigate new image analysis methods, to help address these challenges. In particular, there was a focus on the following topics: Big data problems and solutions Multimodality Dynamic imaging The workshop facilitated the communication of both current opportunities and challenges of new imaging techniques. It also allowed for the sharing of knowledge on current approaches and solutions of mathematical modelling and analysis approaches, with presentations on industry insights and state-of-the-art mathematical techniques for Big Data Analytics. This event was of interest to participants from the biomedical imaging industry, mathematics, engineering, computer science and physics, as well as biology and medicine. |
| Year(s) Of Engagement Activity | 2016 |
| URL | http://www.turing-gateway.cam.ac.uk/event/tgmw32 |
| Description | Panel member at Women in Data Science event at the Isaac Newton Institute, Cambridge |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | The field of Data Science is booming, yet comparatively few women are entering it. Why? What are the obstacles and opportunities facing them if they do? The path to change is challenging, but there are women out there who can testify that it's possible. A Women in Data Science event is being held at the Isaac Newton Institute on Wednesday 7 December within the New Developments in Data Privacy workshop, part of the current INI programme on Data Linkage and Anonymisation. The event included a Women's Round Table Event and Wine Reception Panelists included: Prof Sheila Bird (Medical Research Council) Prof Cynthia Dwork (Microsoft Research and Harvard) Prof Sofia Olhede (UCL) Dr Carola-Bibiane Schönlieb (Cantab Capital Institute for Mathematics of Information, University of Cambridge, and Alan Turing Institute Faculty Fellow) Prof Natalie Shlomo (University of Manchester) |
| Year(s) Of Engagement Activity | 2016 |
| URL | http://www.newton.ac.uk/node/1273254 |
| Description | Re-visioning Transport and Health 2019, Workshop and Hackathon |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | In this workshop and hackathon, we assessed the state of the field and discussed how developments can be made to provide the data decision-makers in addressing the questions of health and sustainability for transport systems and the built environment. The workshop brought together experts in computer vision, earth observation, street-level data collection, population health, cities, and transport studies. The hackathon had two streams. The first stream involved improving/ developing algorithms to solve an image recognition problem and the second required interdisciplinary work to propose how to solve a real-world problem in a lower and middle income country with imaging data. |
| Year(s) Of Engagement Activity | 2019 |
| URL | https://sites.google.com/view/transportcam2019/home/workshop |
| Description | Seeing more in pictures - open mathematics day for Y12 girls |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Schools |
| Results and Impact | Dr Carola Schönlieb gives an insight into some of the mathematics behind image analysis and its wide-ranging applications in fields ranging from developing cancer therapies to restoring artworks, together with some personal reflections on her own career journey through mathematical study and research. Dr Carola Schönlieb is Reader in Applied and Computational Analysis and Head of Cambridge Image Analysis Group at the Department of Applied Mathematics and Theoretical Physics, University of Cambridge. This talk was originally given to an audience of Y12 girls (aged 16-17) at an event for students considering applying to university to study mathematics. The talk was recorded at the Centre for Mathematical Sciences, University of Cambridge, on 18 April 2016. |
| Year(s) Of Engagement Activity | 2016 |
| URL | https://www.youtube.com/watch?v=9SPN9Ouxx7g&feature=youtu.be |
| Description | Talk at Big Data Showcase event in Cambridge on Seeing More in Images: A Mathematical Perspective |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Industry/Business |
| Results and Impact | Background Mathematics underpins so many things we take for granted - smart phones, weather forecasting, architecture, 3D software, structural engineering, sensing technologies, are just a few examples. Indeed, the fruits of mathematical research - such as the resulting techniques and algorithms, affect the daily lives of everyone and the economic impact of mathematics is already well proven. The University of Cambridge's Centre for Mathematical Sciences (CMS) and Big Data Initiative, in partnership with the Turing Gateway to Mathematics highlighted areas of research and expertise in a showcase event, that took place on Wednesday 20th April 2016 at the Centre for Mathematical Sciences in Wilberforce Road, Cambridge. A wide range of talks were given by leading researchers, highlighting areas of mathematical and Big Data sciences. An exhibition ran during the lunch break and the afternoon session. The day ended with a drinks and networking reception between 5.00-6.00PM. The Showcase presented a great opportunity to see what Cambridge has to offer and better understand the diversity and impact that the research in mathematics and big data at Cambridge can make on business and policy across a wide range of areas. Researchers were on hand to discuss specific areas of maths and big data and there was opportunities for delegates to take tours of the GK Batchelor Fluid Dynamics Laboratory and also see the COSMOS Computer. The exhibition included research groups, industrial case studies posters, the EPSRC Centre for Doctoral Training in Analysis, the new Cantab Capital Institute for the Mathematics of Information and details of project opportunities for industry. Aims and Objectives Subjects of talks included industrial areas such as materials and chemical decontamination, mathematical biology, financial maths, cosmology, communications and social sciences. The Showcase presented an excellent opportunity to bring together scientists from mathematics and other disciplines such as physics, chemistry, engineering etc, with interested parties from industry, government and public sectors. The Showcase gave participants a great opportunity to: Meet leading mathematicians and other scientists involved in state-of-the-art mathematical techniques and methods across multiple areas including Big Data Learn more about the potential of mathematics to help provide solutions to real-world problems Find out how to collaborate and partner with the University through research, projects and studentships Network with senior researchers, industry and Government |
| Year(s) Of Engagement Activity | 2016 |
| URL | http://www.turing-gateway.cam.ac.uk/event/tgmw33 |
| Description | Variational models and partial differential equations for mathematical imaging |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | Plenary lecture at the Conference on the Numerical Solution of Differential and Differential-Algebraic Equations (NUMDIFF-15). Variational models and partial differential equations for mathematical imaging: Images are a rich source of beautiful mathematical formalism and analysis. Associated mathematical problems arise in functional and non-smooth analysis, the theory and numerical analysis of partial differential equations, harmonic, stochastic and statistical analysis, and optimisation. Starting with a discussion on the intrinsic structure of images and their mathematical representation, in this talk we will learn about variational models for image analysis and their connection to partial differential equations, and go all the way to the challenges of their mathematical analysis as well as the hurdles for solving these - typically non-smooth - models computationally. The talk is furnished with applications of the introduced models to image de-noising, motion estimation and segmentation, as well as their use in biomedical image reconstruction such as it appears in magnetic resonance imaging. |
| Year(s) Of Engagement Activity | 2018 |
| URL | https://sim.mathematik.uni-halle.de/numdiff/Numdiff15/index.html |
| Description | Winter School: The Mathematics of Imaging 7-11 January, 2019 |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Postgraduate students |
| Results and Impact | Helped to co-organise this Winter school "The mathematics of Imaging", that was held in Paris at the IHP (Institut Henri Poincaré), from January 7 to April 5, 2019. The event included course, practical sessions, flash presentations and posters which created much discussion and hopefully new collaborations. |
| Year(s) Of Engagement Activity | 2019 |
| URL | https://imaging-in-paris.github.io/semester2019/school/ |
| Description | Women in MIUA workshop |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Postgraduate students |
| Results and Impact | The WiMIUA is co-located with the 26th Conference on Medical Image Understanding and Analysis (MIUA 2022). The event provides a unique networking platform for academia and industry including engineers, mathematicians, clinicians and entrepreneurs. The event consists on (e)-poster sessions, invited speakers and social gatherings. |
| Year(s) Of Engagement Activity | 2022 |
| URL | https://www.miua2022.com/WiMIUA |
| Description | Workshop on Gradient flows: challenges and new directions, ICMS 2018 |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Postgraduate students |
| Results and Impact | Gradient flows: challenges and new directions ICMS, The Bayes Centre, 47 Potterrow, Edinburgh EH8 9BT 10 - 14 September 2018 ORGANISERS Bertram Düring, University of Sussex Carola-Bibiane Schönlieb, University of Cambridge Yves van Gennip, University of Nottingham Marie-Therese Wolfram, University of Warwick |
| Year(s) Of Engagement Activity | 2018 |
| URL | https://www.icms.org.uk/gradientflows.php |
| Description | Workshop on High-dimensional Statistics, Inverse Problems and Convex Analysis, Royal Statistical Society, London, UK, 22 March 2016. |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | This workshop will bring together scientists from the statistics, applied mathematics, signal processing and machine learning communities around the topic of convex analysis and its application to challenging inverse problems. The workshop will feature invited talks by world-leading experts presenting cutting edge research on new theory, methodology, and computer algorithms. We aim to provide a valuable opportunity to network and to foster extensive future interaction between the these disciplines. Co-organiser: M. Pereyra. |
| Year(s) Of Engagement Activity | 2016 |
| URL | http://www.bristol.ac.uk/maths/events/2016/high-dimensional-statistics-inverse-problems-and-convex-a... |
| Description | Workshop on Mathematical imaging with partially unknown models, Jesus College in Cambridge, 20-21 Feb. 2017. |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | The CCIMI and CMIH are pleased to be co-sponsoring the Cambridge - Heriot Watt interdisciplinary data science workshop on "Mathematical imaging with partially unknown models" at Jesus College in Cambridge, 20-21 Feb. 2017. More details on the programme will be confirmed at a later date. The workshop is organised by Marcelo Pereyra (Assistant professor, School of Mathematical and Computer Sciences, Heriot Watt) and Carola-Bibiane Schönlieb (Head of the Cantab Capital Institute for the Mathematics of Information (CCIMI), Cambridge), alongside local organiser Martin Benning (Department of Applied Mathematics and Theoretical Physics, Cambridge) The workshop aims to gather an interdisciplinary group of leading imaging experts from the applied analysis, statistics, and signal processing communities around the topic of "imaging with partially unknown models". The goal is to promote synergy and cross-fertilisation between these communities and set the basis for a multidisciplinary approach to the problem. Mathematical imaging is at the core of modern data science, with important applications in medicine, biology, defense, agriculture and environmental sciences. This active research field studies imaging inverse problems involving the estimation of an unobserved true image from measurements that are noisy, incomplete and resolution-limited. This proposal focuses on an increasingly important and particularly challenging class of imaging inverse problems that, in addition to being ill-posed and ill-conditioned, are further complicated by inaccurate and partial knowledge of the observation system and of the properties of the underlying true image (which are essential to regularise the problem and deliver meaningful estimates). These so-called "semi-blind" and "unsupervised" problems are the focus of significant research efforts across a range of scientific communities, particularly applied analysis, Bayesian statistics, and signal processing, which have recently produced important developments in mathematical theory, methods, models and efficient algorithms. The proposed research workshop will focus on three specific aspects of imaging with partially unknown models that will be key in future methodology: learning models from observed data, model comparison and selection in the absence of ground truth, and robust inference with approximate models. Programme; Monday: 9.30 - 10.20: Gabriel Peyré Coffee break (30 minutes) 10.50 - 11.40: Yves Wiaux 11.40 - 12.30: Samuli Siltanen Lunch & Poster session (12.30 - 14.00). Tuesday: 9.30 - 10.20: Silvia Villa Coffee break (30 minutes) 10.50 - 11.40: Juan Carlos de los Reyes 11.40 - 12.30: John Aston Plenary speakers are: Gabriel Peyré (Université Paris-Dauphine) Silvia Villa (Istituto Italiano di Tecnologia and Massachusetts Institute of Technology) Yves Wiaux (Heriot-Watt University) Juan Carlos de los Reyes (Escuela Nacional Politécnica de Quito) John Aston (University of Cambridge) Samuli Siltanen (University of Helsinki) Invited Participants: Yoann Altmann (Heriot Watt, UK) Martin Benning (University of Cambridge, UK) Natalia Bochkina (University of Edinburgh, UK) Matthias Ehrhardt (University of Cambridge, UK) Teresa Klatzer (Graz University of Technology, Austria) Felix Lucka (University College London, UK) Marcelo Pereyra (Heriot Watt, UK) Carola-Bibiane Schönlieb (CCIMI, University of Cambridge, UK) Registrations: Simon Arridge (UCL, UK) Eva-Maria Brinkmann (University of Münster, Germany) Tatiana Alessandra Bubba (University of Helsinki, Finland) Luca Calatroni (Ecole Polytechnique, France) Veronica Corona (University of Cambridge, UK) Jonathan Dunlop (Schlumberger, UK) Silvia Gazzola (University of Bath, UK) Joanna Grah (University of Cambridge, UK) Abderrahim Halimi (Heriot Watt, UK) Karl Harrison (University of Cambridge, UK) Andreas Hauptmann (University of Helsinki, Finland) Jan Holland (Springer-Verlag) Eugenie Hunsicker (Loughborough University, UK) Abdul Jumaat (University of Liverpool, UK) Markus Juvonen (University of Helsinki) Lukas Lang (University of Cambridge, UK) Nguyet Minh Mach (University of Helsinki) Sebastian Neumayer (University of Cambridge, UK) Simone Parisotto (University of Cambridge, UK) Mihaela Pricop-Jeckstadt (TU-Dresden, Germany) Shannon Seah (University of Cambridge, UK) Ferdia Sherry (University of Cambridge, UK) Megan Wilson (University of Cambridge, UK) Joab Winkler (Sheffield University, UK) Evren Yarman (Schlumberger, UK) |
| Year(s) Of Engagement Activity | 2017 |
| URL | http://www.ccimi.maths.cam.ac.uk/events/cambridge-heriot-watt-interdisciplinary-data-science-worksho... |
| Description | Workshop on Statistics, Learning and Variational Methods in Imaging |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Other audiences |
| Results and Impact | Scope: We bring together young researchers with a variational background, statisticians and experts in learning theory to work on the following challenging topics: - statistics of noise and its modelling - modelling a-priori information - learning the above from samples - Bayesian and variational approaches The workshop is setup as a combination of presentations from invited speakers and discussion rounds to drive an exchange between the participants from different research areas involved. |
| Year(s) Of Engagement Activity | 2012 |
| URL | http://www.damtp.cam.ac.uk/user/cbs31/Imaging_Workshop_Cambridge_September_2012/Workshop.html |
| Description | Woudschoten Conference 2021 |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | The Woudschoten conference has a long and rich history, dating back to the first edition in 1976, and it has featured many of the great names in numerical analysis and scientific computing. Since its establishment in the early days of `approximation and discretization' - the two themes of the first edition of the conference -- the Woudschoten conference has provided an introduction to and overview of groundbreaking developments in scientific computing and numerical analysis. The conference is attended by essentially all Dutch and Flemish researchers in numerical analysis and scientific computing, from PhD students to full professors, and including industrial researchers. By virtue of its unique format and its informal setting, the conference does not only provide insight and inspiration to the Dutch-Flemish numerical-mathematics community, but it also plays a central role in retaining coherence in the community. |
| Year(s) Of Engagement Activity | 2021 |
| URL | https://wsc.project.cwi.nl/woudschoten-conferences/2021-conference |