Greedy type algorithms for RIP matrices. A study of two selection rules

TL;DR

This paper explores new greedy algorithms for sparse signal recovery based on the RIP property, introducing a novel selection rule that relaxes RIP restrictions but requires smaller thresholds, supported by experimental results.

Contribution

It introduces a new selection rule for greedy algorithms that reduces RIP restrictions and analyzes its effectiveness for sparse signal approximation.

Findings

New selection rule improves RIP constant restrictions

Smaller threshold parameters are needed for coefficient selection

Experimental results validate the proposed algorithms' effectiveness

Abstract

Some consequences of the Restricted Isometry Property (RIP) of matrices have been applied to develop a greedy algorithm called "ROMP" (Regularized Orthogonal Matching Pursuit) to recover sparse signals and to approximate non-sparse ones. These consequences were subsequently applied to other greedy and thresholding algorithms like "SThresh", "CoSaMP", "StOMP" and "SWCGP". In this paper, we find another consequence of the RIP property and use it to analyze the approximation to k-sparse signals with Stagewise Weak versions of Gradient Pursuit (SWGP), Matching Pursuit (SWMP) and Orthogonal Matching Pursuit (SWOMP). We combine the above mentioned algorithms with another selection rule similar to the ones that have appeared in the literature showing that results are obtained with less restrictions in the RIP constant, but we need a smaller threshold parameter for the coefficients. The results of some experiments are shown.