Variational Bayesian image restoration with group-sparse modeling of wavelet coefficients

Ganchi Zhang, Nick Kingsbury
2015 Digital signal processing (Print)  
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 the
more » ... vex search space. We also integrate our method, variational Bayesian with majorization minimization (VBMM), with tree-structured modeling of the wavelet coefficients. This extension achieves significant gains in performance over the coefficient-sparse version of the algorithm. The experimental results demonstrate that the proposed method and its tree-structured extensions are effective for various imaging applications such as image deconvolution, image superresolution and compressive sensing magnetic resonance imaging (MRI) reconstruction, and that they outperform more conventional sparsityinducing methods based on the l 1 -norm.
doi:10.1016/j.dsp.2015.04.011 fatcat:zxfslb4hmren7ffggich5gc4xi