Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Dictionary Preconditioning for Greedy Algorithms
IEEE Transactions on Signal Processing
Matching pursuits with time-frequency dictionaries
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Recovery of exact sparse representations in the presence of bounded noise
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
Fractal pursuit for compressive sensing signal recovery
Computers and Electrical Engineering
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Sparse approximation in a redundant basis has attracted considerable attention in recent years because of many practical applications. The problem basically involves solving an under-determined system of linear equations under some sparsity constraint. In this paper, we present a simple interpretation of the recently proposed complementary matching pursuit (CMP) algorithm. The interpretation shows that the CMP, unlike the classical MP, selects an atom and determines its weight based on a certain sparsity measure of the resulting residual error. Based on this interpretation, we also derive another simple algorithm which is seen to outperform CMP at low sparsity levels for noisy measurement vectors.