Iterative method for simultaneous sparse approximation

TL;DR

This paper introduces SIMAT, an iterative method for joint sparse signal recovery that outperforms existing algorithms in accuracy and complexity, with practical applications in radar systems.

Contribution

The paper presents a new iterative algorithm, SIMAT, for simultaneous sparse approximation, with proven convergence and superior performance over existing methods.

Findings

SIMAT outperforms SOMP and BIMAT in SNR and success rate.

SIMAT is less complex than BIMAT, suitable for practical applications.

Numerical experiments validate the effectiveness of SIMAT.

Abstract

This paper studies the problem of Simultaneous Sparse Approximation (SSA). This problem arises in many applications which work with multiple signals maintaining some degree of dependency such as radar and sensor networks. In this paper, we introduce a new method towards joint recovery of several independent sparse signals with the same support. We provide an analytical discussion on the convergence of our method called Simultaneous Iterative Method with Adaptive Thresholding (SIMAT). Additionally, we compare our method with other group-sparse reconstruction techniques, i.e., Simultaneous Orthogonal Matching Pursuit (SOMP), and Block Iterative Method with Adaptive Thresholding (BIMAT) through numerical experiments. The simulation results demonstrate that SIMAT outperforms these algorithms in terms of the metrics Signal to Noise Ratio (SNR) and Success Rate (SR). Moreover, SIMAT is considerably less complicated than BIMAT, which makes it feasible for practical applications such as implementation in MIMO radar systems.