Model based variational Bayesian compressive sensing using heavy tailed sparse prior

• We have proposed a new model based Bayesian Compressive Sensing (CS) based on generalized double Pareto.
• We have derived all posterior pdfs׳ parameters of this new model in the closed form.
• We examine the proposed algorithm in two scenarios: without noise and noisy observation.
• In both scenarios, the proposed algorithm outperforms the well-known CS method.

In this paper, a novel multiscale model-based Bayesian compressive sensing is investigated using variational Bayesian inference in the complex wavelet domain. This model preserves the structural information by two-state signal/noise Hidden Markov Tree (HMT). Tree structured hierarchical Generalized Double Pareto (GDP) distribution is used to model the sparsity of the signal. Using the Variational Bayes (VB) inference procedure a closed-form solution is obtained for model parameters. Experimental results in compressive sensing application show that the reconstruction error and CPU time of the proposed algorithm is lower compared to the other well-known algorithms.