Iterative Reweighted Algorithms for Sparse Signal Recovery with Temporally Correlated Source Vectors

Abstract: Iterative reweighted algorithms, as a class of algorithms for sparse signal recovery, have been found to have better performance than their non-reweighted counterparts. However, for solving the problem of multiple measurement vectors (MMVs), all the existing reweighted algorithms do not account for temporal correlation among source vectors and thus their performance degrades significantly in the presence of correlation. In this work we propose an iterative reweighted sparse Bayesian learning (SBL) algorithm exploiting the temporal correlation, and motivated by it, we propose a strategy to improve existing reweighted $\ell_2$ algorithms for the MMV problem, i.e. replacing their row norms with Mahalanobis distance measure. Simulations show that the proposed reweighted SBL algorithm has superior performance, and the proposed improvement strategy is effective for existing reweighted $\ell_2$ algorithms.