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


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Authors

Zhang, Ganchi 
Kingsbury, Nick 

Abstract

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 non-convex 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 sparsity-inducing methods based on the _l1-norm.

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Keywords

Image restoration, Wavelet group-sparse modeling, Variational Bayesian inference, Majorization minimization, Dual-tree complex wavelets

Journal Title

DIGITAL SIGNAL PROCESSING

Conference Name

Journal ISSN

1051-2004
1095-4333

Volume Title

47

Publisher

Elsevier BV