Extensions to compressed sensing theory with application to dynamic MRI
Lead Research Organisation:
University of Edinburgh
Department Name: Sch of Engineering
Abstract
The problem of data acquisition or sampling lies at the heart of digital signal processing. It has been a long held belief that one should acquire a sufficient number of samples to satisfy the so-called Nyquist criterion. Then the discretely sampled signal is an equivalent representation of the original analogue one. However, recently, the paradigm of compressed sensing has challenged this idea. If a signal is known to have structure, and almost all signals do, then this can be used to reduce the number of samples required to define the signal; compressed sensing advocates sampling at the information rate not the Nyquist rate . This project aims to extend the existing theory of compressed sensing to include more general advanced signal models and, in particular, multi-resolution image models. These ideas should have a big impact on problems where sampling data is difficult either because it is time consuming, expensive or has associated safety issues (e.g. patient exposure to electromagnetic radiation). The project will further explore the potential of compressed sensing as a novel compression strategy for possible use in distributed or remote sensing applications. The project will use these ideas to develop new rapid Magnetic Resonance Imaging (MRI) acquisition systems. The advantages of accelerated scan times are manifold. It enables clinicians to take higher resolution scans and to acquire more detailed dynamic image sequences (e.g. for cardiac diagnosis). Furthermore, with the trend to the increased use of high field scanners reducing the samples for a given image acquisition has the additional benefit of lowering the RF exposure that the patient is subjected to.
Organisations
People |
ORCID iD |
| Mike Davies (Principal Investigator) | |
| Ian Marshall (Co-Investigator) |
Publications
Blanchard J
(2012)
Recovery Guarantees for Rank Aware Pursuits
in IEEE Signal Processing Letters
Blumensath T
(2010)
Normalized Iterative Hard Thresholding: Guaranteed Stability and Performance
in IEEE Journal of Selected Topics in Signal Processing
Blumensath T
(2012)
Compressed Sensing - Theory and Applications
Blumensath T
(2009)
Iterative hard thresholding for compressed sensing
in Applied and Computational Harmonic Analysis
Davies M
(2011)
Sample-distortion functions for compressed sensing
Davies M
(2012)
Rank Awareness in Joint Sparse Recovery
in IEEE Transactions on Information Theory
Fabien Millioz
(2011)
Detection and segmentation of fmcw radar signals based on the chirplet transform
Giryes R
(2014)
Greedy-like algorithms for the cosparse analysis model
in Linear Algebra and its Applications
Gribonval R
(2012)
Compressible Distributions for High-Dimensional Statistics
in IEEE Transactions on Information Theory
Kelly S
(2012)
Advanced image formation and processing of partial synthetic aperture radar data
in IET Signal Processing
Marshall I
(2014)
Application of kt-BLAST acceleration to reduce cardiac MR imaging time in healthy and infarcted mice.
in Magma (New York, N.Y.)
Mike Davies (Author)
(2010)
Dictionary learning for sparse representations: A pareto curve root finding approach
Mike Davies (Author)
(2011)
Compressible priors for high-dimensional statistics
in Arxiv preprint arXiv:1102.1249
Mike Davies (Author)
(2011)
Compressed sensing in k-space: from magnetic resonance imaging and synthetic aperture radar
Mike Davies (Author)
(2011)
Sample-distortion functions for compressed sensing
Plumbley M
(2010)
Sparse Representations in Audio and Music: From Coding to Source Separation
in Proceedings of the IEEE
Rilling G
(2013)
Multilattice sampling strategies for region of interest dynamic MRI.
in Magnetic resonance in medicine
Tao Y
(2013)
Carotid blood flow measurement accelerated by compressed sensing: validation in healthy volunteers.
in Magnetic resonance imaging
Yaghoobi M
(2013)
Constrained Overcomplete Analysis Operator Learning for Cosparse Signal Modelling
in IEEE Transactions on Signal Processing
| Description | The project developed a number of theoretical and algorithmic extensions to compressed sensing, including the incorporation of structured sparsity, joint sparsity and advanced measurement strategies. The project also highlighted some of the essential limitations of compressed sensing in providing improved imaging from limited measurements |
| Exploitation Route | Advanced imaging methods have impacted on other imaging domains, including SAR. This project also acted as a precursor for recent work on a compressed sensing framework for magnetic resonance fingerprinting |
| Sectors | Aerospace, Defence and Marine,Digital/Communication/Information Technologies (including Software),Healthcare |