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In this work, we present a recent wavelet-based image restoration framework based on a group-sparse Gaussian scale mixture model. A hierarchical Bayesian estimation is derived using a combination of variational Bayesian inference and a subband-adaptive majorization-minimization method that simplifies computation of the posterior distribution. We show that both of these iterative methods can converge together without needing nested loops, and thus good solutions can be found rapidly in thedoi:10.1016/j.dsp.2015.04.011 fatcat:zxfslb4hmren7ffggich5gc4xi