General Total Variation Regularized Sparse Bayesian Learning for Robust Block-Sparse Signal Recovery

TL;DR

This paper introduces a novel TV-regularized Sparse Bayesian Learning method for robust block-sparse signal recovery that does not require prior knowledge of block sizes or boundaries, demonstrating improved robustness and flexibility.

Contribution

It proposes a new TV-regularized SBL algorithm that regularizes hyperparameters instead of signal components, enabling effective recovery without prior block structure knowledge.

Findings

Robust recovery of block-sparse signals with unknown structures.

Effective for signals with both block-patterned and isolated components.

Algorithm employs convex optimization, ensuring computational flexibility.

Abstract

Block-sparse signal recovery without knowledge of block sizes and boundaries, such as those encountered in multi-antenna mmWave channel models, is a hard problem for compressed sensing (CS) algorithms. We propose a novel Sparse Bayesian Learning (SBL) method for block-sparse recovery based on popular CS based regularizers with the function input variable related to total variation (TV). Contrary to conventional approaches that impose the regularization on the signal components, we regularize the SBL hyperparameters. This iterative TV-regularized SBL algorithm employs a majorization-minimization approach and reduces each iteration to a convex optimization problem, enabling a flexible choice of numerical solvers. The numerical results illustrate that the TV-regularized SBL algorithm is robust to the nature of the block structure and able to recover signals with both block-patterned and isolated components, proving useful for various signal recovery systems.