Matrix analysis
Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
Matrix computations (3rd ed.)
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Machine Learning
Sparse bayesian learning and the relevance vector machine
The Journal of Machine Learning Research
Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit
Foundations of Computational Mathematics
Probing the Pareto Frontier for Basis Pursuit Solutions
SIAM Journal on Scientific Computing
Linear convergence of the conjugate gradient method
IBM Journal of Research and Development
Sparse Bayesian learning for basis selection
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Quantized overcomplete expansions in IRN: analysis, synthesis, and algorithms
IEEE Transactions on Information Theory
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
Decoding by linear programming
IEEE Transactions on Information Theory
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
On the exponential convergence of matching pursuits in quasi-incoherent dictionaries
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration
IEEE Transactions on Image Processing
IEEE Transactions on Information Theory
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Finding sparse solutions to underdetermined inverse problems is a fundamental challenge encountered in a wide range of signal processing applications, from signal acquisition to source separation. This paper looks at greedy algorithms that are applicable to very large problems. The main contribution is the development of a new selection strategy (called stagewise weak selection) that effectively selects several elements in each iteration. The new selection strategy is based on the realization that many classical proofs for recovery of sparse signals can be trivially extended to the new setting. What is more, simulation studies show the computational benefits and good performance of the approach. This strategy can be used in several greedy algorithms, and we argue for the use within the gradient pursuit framework in which selected coefficients are updated using a conjugate update direction. For this update, we present a fast implementation and novel convergence result.