Multi-Task Sparse Signal Recovery with Dirichlet Process Priors Based on Expectation Propagation Technique

Abstract

Exploiting the shared information among tasks to significantly improve the sparse reconstruction performance lays the essence of multi-task compressive sensing. In this paper, a novel generative model of multi-task compressive sensing with Dirichlet process (DP) priors is proposed and the sharing mechanisms among tasks are revealed, yielding a principled means of inferring the clusters as well as performing compressive sensing inversion simultaneously. The spike-and-slab priors are first used to model the group sparsity among tasks within the identical cluster, and the DP priors are then introduced to automatically perform clustering for the tasks. The expectation propagation method is finally carried out to take the inference for posterior distribution approximation. The superiority of the proposed method over state-of-the-art algorithms is demonstrated by using experimental results on both numerical data and real data sets.