Multiple Orthogonal Least Squares for Joint Sparse Recovery

Abstract

Joint sparse recovery aims to reconstruct multiple sparse signals having a common support using multiple measurement vectors (MMV). In this paper, we propose a robust joint sparse recovery algorithm, termed MMV multiple orthogonal least squares (MMV-MOLS). Owing to the novel identification rule that fully exploits the correlation between the measurement vectors, MMV-MOLS greatly improves the accuracy of the recovered signals over the conventional joint sparse recovery techniques. From the simulation results, we show that MMV-MOLS outperforms conventional joint sparse recovery algorithms, in both full row rank and rank deficient scenarios. In our analysis, we show that MMV-MOLS recovers any row $K$ -sparse matrix accurately in the full row rank scenario with m = K + 1 measurements, which is, in fact, the minimum number of measurements to recover a row $K$ -sparse matrix. In addition, we analyze the performance guarantee of the MMV-MOLS algorithm in the rank deficient scenario using the restricted isometry property (RIP).