EPSRC-Royal Society fellowship engagement (2012): From Spectra to Sampling - Functional Analysis meets Applied Harmonic Analysis
Lead Research Organisation:
University of Cambridge
Department Name: Applied Maths and Theoretical Physics
Abstract
Please refer to attached Royal Society application
Planned Impact
Please refer to attached Royal Society application
People |
ORCID iD |
| Anders Hansen (Principal Investigator / Fellow) |
Publications
Adcock B
(2015)
Generalized Sampling and Infinite-Dimensional Compressed Sensing
in Foundations of Computational Mathematics
Adcock B
(2016)
A Note on Compressed Sensing of Structured Sparse Wavelet Coefficients From Subsampled Fourier Measurements
in IEEE Signal Processing Letters
Adcock B
(2014)
On Stable Reconstructions from Nonuniform Fourier Measurements
in SIAM Journal on Imaging Sciences
Adcock B
(2017)
Weighted frames of exponentials and stable recovery of multidimensional functions from nonuniform Fourier samples
in Applied and Computational Harmonic Analysis
Adcock B
(2016)
Density Theorems for Nonuniform Sampling of Bandlimited Functions Using Derivatives or Bunched Measurements
in Journal of Fourier Analysis and Applications
Adcock B
(2013)
Beyond Consistent Reconstructions: Optimality and Sharp Bounds for Generalized Sampling, and Application to the Uniform Resampling Problem
in SIAM Journal on Mathematical Analysis
Adcock B
(2021)
Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling
in Applied and Computational Harmonic Analysis
Adcock B
(2015)
Compressed Sensing and its Applications - MATHEON Workshop 2013
| Description | The main discovery of the project has been a mathematical theory to optimise sampling strategies used in medical imaging (e.g. MRI) that allows for speedup of the acquisition time as well as resolution enhancing of the images. This allows for substantial time reduction in medical imaging as well as better image quality, which again may lead to more accurate diagnosis of patients. |
| Exploitation Route | The mathematical theory is developed for a technique called compressed sensing. This techniques was in 2017 approved by the US Food and Drug Administration for use in MRI. As a result, all the major producers of MRI machines have implemented this technique in their machines. |
| Sectors | Healthcare |
| Description | Siemens, one of the largest manufacturers of medical imaging equipments, has already implemented the methods provided by this research project on their MRI machines. As a result of the US Food and Drug Administration's approval of compressed sensing for commercial use in MRI machines, these techniques are now universally implemented across all manufacturers. Our theoretical development provides the understanding of why and how this works, and allows for optimal use. |
| Sector | Healthcare |
| Impact Types | Societal,Economic |
| Description | Resolution enhancing in MRI |
| Organisation | University of Cambridge |
| Department | Department of Radiology |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | We have developed a mathematical theory that shows how one can enhance resolution in Magnetic Resonance Imaging. We have also implemented this in software that can be readily used for practitioners. |
| Collaborator Contribution | Our partners at the radiology department have provided us with data and expertise on MRI machines in order to optimize our method for use in practice. Our partners will now use the method in clinical trials. |
| Impact | Besides the clinical trials that are now in the planning stage, our collaboration won the University of Cambridge nomination for the prestigious Rosetree Award. |
| Start Year | 2015 |