Markov-tree Bayesian group-sparse modeling with wavelets

In this paper, we propose a new Markov-tree Bayesian modeling of wavelet coefficients. Based on a group-sparse Gaussian Scale Mixtures model with 2-layer cascaded Gamma distributions for the variances, the proposed method effectively exploits both intrascale and interscale relationships across wavelet subbands. To determine the posterior distribution, we apply Variational Bayesian inference with a subband adaptive majorization-minimization method to make the method tractable for large problems.