Robust Recovery of Structured Sparse Signals With Uncertain Sensing Matrix: A Turbo-VBI Approach

In many applications in wireless communications, we need to recover a structured sparse signal from a linear measurement model with uncertain sensing matrix. There are two challenges of designing an algorithm framework for this problem. How to choose a flexible yet tractable sparse prior to capture different structured sparsities in specific applications? How to handle a sensing matrix with uncertain parameters and possibly correlated entries? As will be explained in the introduction, existing common methods in compressive sensing (CS), such as approximate message passing (AMP) and variational Bayesian inference (VBI), may not work well. To better address this problem, we propose a novel Turbo-VBI algorithm framework, in which a three-layer hierarchical structured (3LHS) sparse prior model is proposed to capture various structured sparsities that may occur in practice. By combining the message passing and VBI approaches via the turbo framework, the proposed Turbo-VBI algorithm is able to fully exploit the structured sparsity (as captured by the 3LHS sparse prior) for robust recovery of structured sparse signals under an uncertain sensing matrix. Finally, we apply the Turbo-VBI framework to solve two application problems in wireless communications and demonstrate its significant gain over the state-of-art CS algorithms.