CoSaMP: Iterative signal recovery from incomplete and inaccurate samples

TL;DR

CoSaMP is an efficient iterative algorithm for reconstructing compressible signals from incomplete and noisy samples, providing guarantees comparable to optimization methods with low computational complexity.

Contribution

The paper introduces CoSaMP, a new iterative recovery algorithm that matches the performance of optimization-based approaches while being computationally efficient and practical for large-scale problems.

Findings

Provides rigorous recovery guarantees.

Achieves near-linear computational complexity.

Demonstrates practical efficiency for large signals.

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.