Structured Bayesian learning for recovery of clustered sparse signal

Abstract

This paper considers the problem of recovering sparse signals with cluster structure of unknown sizes and locations. A hybrid prior is proposed by introducing a local continuity indicator, which adaptively imposes cluster information on the sparse coefficients according to the inherent data structure. The local continuity indicator flexibly switches the prior for a sparse coefficient between a fully pattern-coupled one and an independent one, so that the estimation of the sparse coefficient can selectively use the statistical information of its neighbors. Variational Bayesian inference is used to estimate the hidden variables based on the constructed probabilistic modeling. Numerical results of comprehensive simulations and real data experiments demonstrate that the proposed algorithm can effectively avoid the problem of structural mismatch and outperform other recently reported clustered sparse signal recovery algorithms in noisy environments.