A Variational Bayesian EM Approach to Structured Sparse Signal Reconstruction

This paper investigates a variational Bayesian expectation maximization (VBEM) scheme to reconstruct structured sparse signals. To fully exploit available signal priors, the structured sparsity combines sparsity prior and structure prior together. In contrast to recent studies, inferring the unobserved variables via Markov chain Monte Carlo (MCMC) which demands infinite iterations to converge, this work employs probabilistic graphic models (PGMs) to factorize the complex joint distributions of signal models and utilizes VBEM algorithm to optimize the lower bound of the model marginal likelihood. In this way, analytical posterior distributions of signal coefficients and model parameters can be obtained by a two-step iterative algorithm. The proposed method reduces computational time consumption with little reconstruction performance loss compared to long-time MCMC, and outperforms state-of-art recovery algorithms. Thus, it offers a practical and stable approach to large-scale Bayesian recovery applications.