Block-Sparse Signal Recovery via General Total Variation Regularized Sparse Bayesian Learning

Abstract

One of the main challenges in block-sparse signal recovery, as encountered in, e.g., multi-antenna mmWave channel models, is block-patterned estimation <i>without knowledge of block sizes and boundaries</i>. We propose a novel Sparse Bayesian Learning (SBL) method for block-sparse signal recovery under unknown block patterns. Contrary to conventional approaches that impose block-promoting regularization on the signal components, we apply two classes of <i>hyperparameter</i> regularizers for the SBL cost function, inspired by total variation (TV) denoising. The first class relies on a conventional TV difference unit and allows performing the SBL inference iteratively through a set of convex optimization problems, enabling a flexible choice of numerical solvers. The second class incorporates a region-aware TV penalty to penalize the signal and zero blocks in a dissimilar manner, enhancing the performance. We derive an alternating optimization algorithm based on expectation-maximization to perform the SBL inference through computationally efficient parallel updates for both the regularizer classes. The numerical results show that the proposed TV-regularized SBL algorithm is robust to the nature of the block structure and is capable of recovering signals with both block-patterned and isolated components, proving effective for various signal recovery systems.