Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Convex Optimization
Algorithms for simultaneous sparse approximation: part I: Greedy pursuit
Signal Processing - Sparse approximations in signal and image processing
Sparse solutions to linear inverse problems with multiple measurement vectors
IEEE Transactions on Signal Processing
On sparse representations in arbitrary redundant bases
IEEE Transactions on Information Theory
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Recovery of exact sparse representations in the presence of bounded noise
IEEE Transactions on Information Theory
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
Algorithms for simultaneous sparse approximation: part I: Greedy pursuit
Signal Processing - Sparse approximations in signal and image processing
Adaptive iterative thresholding algorithms for magnetoencephalography (MEG)
Journal of Computational and Applied Mathematics
Morphological Diversity and Sparsity for Multichannel Data Restoration
Journal of Mathematical Imaging and Vision
An efficient projection for l1, ∞ regularization
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
IEEE Transactions on Signal Processing
Blind multiband signal reconstruction: compressed sensing for analog signals
IEEE Transactions on Signal Processing
On the reconstruction of block-sparse signals with an optimal number of measurements
IEEE Transactions on Signal Processing
IEEE Transactions on Image Processing
Compressive-projection principal component analysis
IEEE Transactions on Image Processing
Sampling theorems for signals from the union of finite-dimensional linear subspaces
IEEE Transactions on Information Theory
Block sparsity and sampling over a union of subspaces
DSP'09 Proceedings of the 16th international conference on Digital Signal Processing
Compressed sensing of time-varying signals
DSP'09 Proceedings of the 16th international conference on Digital Signal Processing
Robust recovery of signals from a structured union of subspaces
IEEE Transactions on Information Theory
Online Learning for Matrix Factorization and Sparse Coding
The Journal of Machine Learning Research
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Learning sparse representation using iterative subspace identification
IEEE Transactions on Signal Processing
Average case analysis of multichannel sparse recovery using convex relaxation
IEEE Transactions on Information Theory
Theoretical and empirical results for recovery from multiple measurements
IEEE Transactions on Information Theory
Direction-of-arrival estimation using a mixed l2,0norm approximation
IEEE Transactions on Signal Processing
Performance analysis for sparse support recovery
IEEE Transactions on Information Theory
SIAM Journal on Scientific Computing
A Bayesian Lasso via reversible-jump MCMC
Signal Processing
Fast Projections onto l1,q-norm balls for grouped feature selection
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part III
Large Scale Bayesian Inference and Experimental Design for Sparse Linear Models
SIAM Journal on Imaging Sciences
Locally Parallel Texture Modeling
SIAM Journal on Imaging Sciences
Compressive sensing based sub-mm accuracy UWB positioning systems: A space-time approach
Digital Signal Processing
Efficient feedback scheme based on compressed sensing in MIMO wireless networks
Computers and Electrical Engineering
Block-sparse recovery via redundant block OMP
Signal Processing
A note on sparse least-squares regression
Information Processing Letters
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A simultaneous sparse approximation problem requests a good approximation of several input signals at once using different linear combinations of the same elementary signals. At the same time, the problem balances the error in approximation against the total number of elementary signals that participate. These elementary signals typically model coherent structures in the input signals, and they are chosen from a large, linearly dependent collection.The first part of this paper presents theoretical and numerical results for a greedy pursuit algorithm, called simultaneous orthogonal matching pursuit.The second part of the paper develops another algorithmic approach called convex relaxation. This method replaces the combinatorial simultaneous sparse approximation problem with a closely related convex program that can be solved efficiently with standard mathematical programming software. The paper develops conditions under which convex relaxation computes good solutions to simultaneous sparse approximation problems.