Generalized Orthogonal Matching Pursuit

TL;DR

This paper introduces a generalized orthogonal matching pursuit (gOMP) algorithm that improves sparse signal recovery efficiency by selecting multiple indices per iteration, achieving comparable performance to $ ext{l}_1$-minimization with faster processing.

Contribution

The paper proposes gOMP, an extension of OMP that selects multiple indices per iteration, reducing the number of iterations needed for sparse signal reconstruction.

Findings

gOMP can perfectly reconstruct $K$-sparse signals under RIP conditions.

Empirical results show gOMP's recovery performance is comparable to $ ext{l}_1$-minimization.

gOMP offers faster processing with competitive computational complexity.

Abstract

As a greedy algorithm to recover sparse signals from compressed measurements, orthogonal matching pursuit (OMP) algorithm has received much attention in recent years. In this paper, we introduce an extension of the OMP for pursuing efficiency in reconstructing sparse signals. Our approach, henceforth referred to as generalized OMP (gOMP), is literally a generalization of the OMP in the sense that multiple $N$ indices are identified per iteration. Owing to the selection of multiple ''correct'' indices, the gOMP algorithm is finished with much smaller number of iterations when compared to the OMP. We show that the gOMP can perfectly reconstruct any $K$-sparse signals ($K > 1$), provided that the sensing matrix satisfies the RIP with $\delta_{NK} < \frac{\sqrt{N}}{\sqrt{K} + 3 \sqrt{N}}$. We also demonstrate by empirical simulations that the gOMP has excellent recovery performance comparable to $\ell_1$-minimization technique with fast processing speed and competitive computational complexity.