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

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