Recovery of Block-Sparse Representations from Noisy Observations via Orthogonal Matching Pursuit

TL;DR

This paper analyzes a block-orthogonal matching pursuit method for recovering block-sparse signals from noisy measurements, demonstrating improved recovery conditions and validating results through numerical experiments.

Contribution

It introduces a block-OMP algorithm with theoretical guarantees for noisy block-sparse signal recovery, highlighting advantages over traditional methods.

Findings

Block-OMP successfully recovers block-sparse signals under certain conditions.

Exploiting block structure enhances recovery performance.

Numerical results confirm theoretical improvements.

Abstract

We study the problem of recovering the sparsity pattern of block-sparse signals from noise-corrupted measurements. A simple, efficient recovery method, namely, a block-version of the orthogonal matching pursuit (OMP) method, is considered in this paper and its behavior for recovering the block-sparsity pattern is analyzed. We provide sufficient conditions under which the block-version of the OMP can successfully recover the block-sparse representations in the presence of noise. Our analysis reveals that exploiting block-sparsity can improve the recovery ability and lead to a guaranteed recovery for a higher sparsity level. Numerical results are presented to corroborate our theoretical claim.