Retrieval of Sparse Solutions of Multiple-Measurement Vectors via Zero-point Attracting Projection

TL;DR

This paper introduces a novel iterative algorithm for sparse signal recovery in MMV problems, combining zero-point attraction with projection and adaptive step sizing to enhance accuracy and convergence speed.

Contribution

The proposed ZAP-based algorithm innovatively integrates gradient attraction and projection with variable step size for improved MMV sparse recovery.

Findings

Outperforms existing algorithms in simulation tests

Achieves higher recovery accuracy and faster convergence

Effective in practical applications like Modulated Wideband Converter

Abstract

A new sparse signal recovery algorithm for multiple-measurement vectors (MMV) problem is proposed in this paper. The sparse representation is iteratively drawn based on the idea of zero-point attracting projection (ZAP). In each iteration, the solution is first updated along the negative gradient direction of an approximate $\ell_{2,0}$ norm to encourage sparsity, and then projected to the solution space to satisfy the under-determined equation. A variable step size scheme is adopted further to accelerate the convergence as well as to improve the recovery accuracy. Numerical simulations demonstrate that the performance of the proposed algorithm exceeds the references in various aspects, as well as when applied to the Modulated Wideband Converter, where recovering MMV problem is crucial to its performance.