Generalized Residual Ratio Thresholding

TL;DR

This paper introduces generalized residual ratio thresholding (GRRT), a new method enabling SOMP and BOMP algorithms to recover sparse signals accurately without prior knowledge of sparsity or noise levels, with proven guarantees.

Contribution

The paper proposes GRRT, a novel thresholding technique that removes the need for prior sparsity and noise variance knowledge in SOMP and BOMP, with theoretical support.

Findings

GRRT achieves support recovery comparable to methods with prior knowledge.

Finite sample and SNR guarantees are derived for GRRT.

Numerical results confirm GRRT's effectiveness in practical scenarios.

Abstract

Simultaneous orthogonal matching pursuit (SOMP) and block OMP (BOMP) are two widely used techniques for sparse support recovery in multiple measurement vector (MMV) and block sparse (BS) models respectively. For optimal performance, both SOMP and BOMP require \textit{a priori} knowledge of signal sparsity or noise variance. However, sparsity and noise variance are unavailable in most practical applications. This letter presents a novel technique called generalized residual ratio thresholding (GRRT) for operating SOMP and BOMP without the \textit{a priori} knowledge of signal sparsity and noise variance and derive finite sample and finite signal to noise ratio (SNR) guarantees for exact support recovery. Numerical simulations indicate that GRRT performs similar to BOMP and SOMP with \textit{a priori} knowledge of signal and noise statistics.