Journal
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
Volume 26, Issue 3, Pages 301-321Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.acha.2008.07.002
Keywords
Algorithms; Approximation; Basis pursuit; Compressed sensing; Orthogonal matching pursuit; Restricted isometry property; Signal recovery; Sparse approximation; Uncertainty principle
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Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples. This paper describes a new iterative recovery algorithm called CoSaMP that delivers the same guarantees as the best optimization-based approaches. Moreover, this algorithm offers rigorous bounds on computational cost and storage. It is likely to be extremely efficient for practical problems because it requires only matrix-vector multiplies with the sampling matrix. For compressible signals, the running time is just C(N log(2) N), where N is the length of the signal. Published by Elsevier Inc.
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