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Alternating Direction Method for Balanced Image Restoration

Authors: Shoulie Xie; Susanto Rahardja;

Alternating Direction Method for Balanced Image Restoration

Abstract

This paper presents an efficient algorithm for solving a balanced regularization problem in the frame-based image restoration. The balanced regularization is usually formulated as a minimization problem, involving an l(2) data-fidelity term, an l(1) regularizer on sparsity of frame coefficients, and a penalty on distance of sparse frame coefficients to the range of the frame operator. In image restoration, the balanced regularization approach bridges the synthesis-based and analysis-based approaches, and balances the fidelity, sparsity, and smoothness of the solution. Our proposed algorithm for solving the balanced optimal problem is based on a variable splitting strategy and the classical alternating direction method. This paper shows that the proposed algorithm is fast and efficient in solving the standard image restoration with balanced regularization. More precisely, a regularized version of the Hessian matrix of the l(2) data-fidelity term is involved, and by exploiting the related fast tight Parseval frame and the special structures of the observation matrices, the regularized Hessian matrix can perform quite efficiently for the frame-based standard image restoration applications, such as circular deconvolution in image deblurring and missing samples in image inpainting. Numerical simulations illustrate the efficiency of our proposed algorithm in the frame-based image restoration with balanced regularization.

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Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
24
Top 10%
Top 10%
Top 10%
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