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 of block sizes and boundaries. 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 hyperparameter 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.