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CoSaMP: Iterative signal recovery from incomplete and inaccurate samples
Authors:D Needell  JA Tropp  
Institution:aDepartment of Mathematics, University of California at Davis, 1 Shields Ave., Davis, CA 95616, USA;bApplied and Computational Mathematics, MC 217-50, California Institute of Technology, Pasadena, CA 91125, USA
Abstract: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(Nlog2N), where N is the length of the signal.
Keywords:Algorithms  Approximation  Basis pursuit  Compressed sensing  Orthogonal matching pursuit  Restricted isometry property  Signal recovery  Sparse approximation  Uncertainty principle
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