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.

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.

Publications

10 25 50
 
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' that is currently advertised see http://www.jobs.cam.ac.uk/job/13010/ and NPL funding for a PostDoc for 3 years on "Imaging" who will start in April 2018. 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 http://www.ccimi.maths.cam.ac.uk and PhD students in Cambridge working on industrial projects with them. 3. We had several new industrial links with McLaren, Unilever and two new start up companies Zedsen and Iolight which are currently at various stages of development. For Zedsen I have started a consultancy with them from spring 2016 which is still ongoing. With Iolight 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/ With Unilever we co-supervised a summer student in 2017 whose project has resulted in Unilever putting forward funding for a one-year Postdoc (to be advertised shortly). We also have ongoing collaborations with healthcare companies such as Astrazeneca, GSK and Toshiba. With Astrazeneca we successfully applied for a more than one million pound funding for establishing a research network on non-local data analysis methods. Moreover, we have a long standing collaboration with Schlumberger Gould Research in Cambridge which resulted in several joint supervisions of internship projects and lately also in a jointly supervised PhD student project. 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. 6. In the course of an EPSRC Healthcare Impact Award we will investigate 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.
First Year Of Impact 2018
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 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 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 Academic/University
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 Academic/University
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 Academic/University
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 Learned Society
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 Learned Society
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 Academic/University
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 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 Turing seed funding for Personalized Breast Cancer Screening
Amount £24,000 (CLF)
Organisation Alan Turing Institute 
Sector Academic/University
Country Unknown
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
 
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 "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
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 Private 
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 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 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 CarolaBibiane 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 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 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 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 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 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:
CarolaBibiane 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 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 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 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 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 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