Localized Low-Rank Promoting for Recovery of Block-Sparse Signals with Intrablock Correlation

We consider the problem of recovering block-sparse signals with intrablock correlated entries. The block partition of the sparse signal is assumed unknown a priori. To exploit the block-sparse structure as well as the local smoothness of the sparse signal, consecutive coefficients of the sparse signal are organized into a number of 2× 2 matrices, and the log-determinant function is used to promote the low rankness of these 2×2 matrices. We show that such a log-determinant function has the ability to promote the block-sparsity and local smoothness simultaneously. An iterative reweighted method is developed by iteratively minimizing a surrogate function of the original objective function. Simulation results show that our proposed method offers competitive performance for recovering block-sparse signals with intrablock correlated entries.