Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing
@article{Adcock2013BreakingTC, title={Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing}, author={B. Adcock and A. Hansen and C. Poon and B. Roman}, journal={ArXiv}, year={2013}, volume={abs/1302.0561} }
We introduce a mathematical framework that bridges a substantial gap between compressed sensing theory and its current use in real-world applications. Although completely general, one of the principal applications for our framework is the Magnetic Resonance Imaging (MRI) problem. Our theory provides a comprehensive explanation for the abundance of numerical evidence demonstrating the advantage of so-called variable density sampling strategies in compressive MRI. Besides this, another important… CONTINUE READING
Figures and Topics from this paper
Figures
62 Citations
On Asymptotic Incoherence and Its Implications for Compressed Sensing of Inverse Problems
- Mathematics, Computer Science
- IEEE Transactions on Information Theory
- 2016
- 7
- PDF
Generalized sampling: stable reconstructions, inverse problems and compressed sensing over the continuum
- Mathematics, Computer Science
- ArXiv
- 2013
- 33
- PDF
Generalized Sampling and Infinite-Dimensional Compressed Sensing
- Mathematics, Computer Science
- Found. Comput. Math.
- 2016
- 127
- PDF
Stable and Robust Sampling Strategies for Compressive Imaging
- Computer Science, Mathematics
- IEEE Transactions on Image Processing
- 2014
- 137
- PDF
On Compressive orthonormal Sensing
- Mathematics, Computer Science
- 2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
- 2016
- 2
- PDF
Compressed solving: A numerical approximation technique for elliptic PDEs based on Compressed Sensing
- Mathematics, Computer Science
- Comput. Math. Appl.
- 2015
- 12
References
SHOWING 1-10 OF 50 REFERENCES
On Variable Density Compressive Sampling
- Mathematics, Computer Science
- IEEE Signal Processing Letters
- 2011
- 81
- PDF
Structured Compressed Sensing: From Theory to Applications
- Computer Science, Mathematics
- IEEE Transactions on Signal Processing
- 2011
- 850
- PDF
A Probabilistic and RIPless Theory of Compressed Sensing
- Mathematics, Computer Science
- IEEE Transactions on Information Theory
- 2011
- 439
- PDF
Model-Based Compressive Sensing
- Mathematics, Computer Science
- IEEE Transactions on Information Theory
- 2010
- 1,515
- PDF
Sensitivity to Basis Mismatch in Compressed Sensing
- Mathematics, Computer Science
- IEEE Trans. Signal Process.
- 2011
- 416
Spread Spectrum Magnetic Resonance Imaging
- Computer Science, Medicine
- IEEE Transactions on Medical Imaging
- 2012
- 67
- PDF
Variable density compressed image sampling
- Mathematics, Medicine
- 2009 17th European Signal Processing Conference
- 2009
- 104
- PDF
Sparse MRI: The application of compressed sensing for rapid MR imaging
- Mathematics, Medicine
- Magnetic resonance in medicine
- 2007
- 5,016
- PDF