Retrieval of sparse solutions of multiple-measurement vectors via zero-point attracting projection

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 ℓ2,0ℓ2,0 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.

► We extend the zero-point attracting projection algorithm to solve the MMV problem. ► An approximate ℓ2,0ℓ2,0 norm is adopted as the penalty to encourage sparsity. ► A step size control scheme is introduced for acceleration at given recovery accuracy. ► The choices of parameters and related criterions are discussed briefly. ► Simulations reveal that the proposed algorithm outperforms some available ones.