A Quasi-Orthogonal Matching Pursuit Algorithm for Compressive Sensing

TL;DR

This paper introduces a quasi-orthogonal matching pursuit algorithm that improves sparse signal recovery performance in compressive sensing, especially under certain matrix conditions, outperforming classical methods in accuracy.

Contribution

The paper proposes a novel quasi-OMP algorithm that enhances recovery success and efficiency compared to traditional OMP, with theoretical guarantees and empirical validation.

Findings

QOMP recovers s-sparse signals within s iterations under certain conditions.

Residual norm decreases linearly with matrix size in Gaussian sensing matrices.

QOMP outperforms classical OMP and GOMP in numerical experiments.

Abstract

In this paper, we propose a new orthogonal matching pursuit algorithm called quasi-OMP algorithm which greatly enhances the performance of classical orthogonal matching pursuit (OMP) algorithm, at some cost of computational complexity. We are able to show that under some sufficient conditions of mutual coherence of the sensing matrix, the QOMP Algorithm succeeds in recovering the s-sparse signal vector x within s iterations where a total number of 2s columns are selected under the both noiseless and noisy settings. In addition, we show that for Gaussian sensing matrix, the norm of the residual of each iteration will go to zero linearly depends on the size of the matrix with high probability. The numerical experiments are demonstrated to show the effectiveness of QOMP algorithm in recovering sparse solutions which outperforms the classic OMP and GOMP algorithm.