An Iteratively Reweighted Method for Recovery of Block-Sparse Signal with Unknown Block Partition

In this paper, a new iteratively reweighted least squares method is proposed for recovery of block-sparse signals with unknown cluster patterns. In many practical applications, sparse signals have block-sparse structures with nonzero coefficients occurring in clusters, while the prior information of the cluster pattern is usually unavailable. To address this issue, we propose an element-overlapping log-sum functional to encourage the sparseness and the cluster pattern simultaneously. The algorithm is developed by iteratively minimizing a convex surrogate function that majorizes the original objective function, which results in an iteratively reweighted process that alternates between estimating the sparse signal and refining the weights of the surrogate function. Convergence of the iterations to a local minimum of the penalty function is also guaranteed. Numerical results are provided to illustrate the effectiveness of the proposed method.