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Zbl 1163.94003
Needell, D.; Tropp, J.A.
CoSaMP: Iterative signal recovery from incomplete and inaccurate samples. (English)
[J] Appl. Comput. Harmon. Anal. 26, No. 3, 301-321 (2009). ISSN 1063-5203

Summary: 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 $O(N\log ^{2}N)$, where $N$ is the length of the signal.

MSC 2000:: *94A12 Signal theory

Keywords: algorithms; approximation; basis pursuit; compressed sensing; orthogonal matching pursuit; restricted isometry property; signal recovery; sparse approximation; uncertainty principle

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Zentralblatt MATH Berlin [Germany]