Multi-Task Bayesian compressive sensing exploiting signal structures

摘要

Conventional Bayesian compressive sensing (CS) is considered for signals that are sparse in some domains, and only sparse prior is adopted to guarantee the exact inverse recovery. However, many additional statistical structures of the signals are naturally available, such as the group structure and the tree structure. In this paper, a novel multi-task structured Bayesian compressive sensing (MTSBCS) algorithm based on a hierarchical Bayesian model is proposed to recover sparse signal, with the exploitation of both intra-group correlation and underlying continuous structure. In this model, two Toeplitz matrix are used to model such intra-group correlation and underlying continuous structure, respectively. According to the proposed generative model, a greedy-based adaptive matching pursuit technique is then introduced to perform the inference for this non-convex optimization problem. Simulations and experimental results show the superiorities of the proposed MTSBCS over several state-of-the-art algorithms.