Structured Bayesian compressive sensing exploiting dirichlet process priors

Abstract

Conventional multi-task Bayesian compressive sensing methods, which compute the sparse representations of signals with a group sparse pattern, generally ignore the inner sparse structures of signals and/or their statistical correlations. These structures are naturally exhibited among clustered tasks with different sparse patterns. In this paper, a novel structured and clustered multi-task compressive sensing framework based on a hierarchical Bayesian model is proposed to exploit the inner sparse pattern and the statistical dependence between tasks. This is achieved by adopting a signal model that exploits the spike-and-slab priors and the Dirichlet Process priors. The former encode sparse patterns of the signals and are further generalized by imposing the Gaussian process for modeling inner structures. The Dirichlet Process priors, on the other hand, imposed on the support reveal the clustering mechanisms among tasks. In so doing, these priors provide a new means to simultaneously infer the clusters and perform compressive sensing inversion, yielding enhanced sparse reconstruction performance. A new inference scheme based on expectation propagation is derived to approximate the posterior distribution for simplifying the computation and deriving analytical expression. Experimental results verify the performance superiorities of the proposed algorithm over existing state-of-the-art methods.