CoSaMP: Iterative Signal Recovery from Incomplete and Inaccurate Samples
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 many cases of interest, the running time is just O(N*log^2(N)), where N is the length of the signal.
Summary¶
Introduces CoSaMP, a greedy sparse-recovery algorithm with provable accuracy, stability, and runtime guarantees under standard compressed-sensing assumptions. It combines matching-pursuit style support identification with least-squares refinement and pruning.