Multi-task Adaptive Matching Pursuit for Sparse Signal Recovery Exploiting Signal Structures

Multi-task compressive sensing is a framework that, by leveraging the useful information contained in multiple tasks, significantly reduces the number of measurements required for sparse signal recovery and achieves improved sparse reconstruction performance of all tasks. In this paper, a novel multi-task adaptive matching pursuit (MT-AMP) algorithm based on a hierarchical Bayesian model is proposed with the exploitation of both the group structure across different tasks and the intra-group correlation, yielding an effective means to simultaneously perform sparse recovery as well as learn the statistical inter-task and intra-group relationships. Experimental results using both synthetic data and real data sets demonstrate the superiorities of the proposed method over existing state-of-the-art algorithms.