Solving Constrained Total-variation Image Restoration and Reconstruction Problems via Alternating Direction Methods

Citation data:

SIAM Journal on Scientific Computing, ISSN: 1064-8275, Vol: 32, Issue: 5, Page: 2710-2736

Publication Year:
2010
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Repository URL:
https://repository.hkbu.edu.hk/hkbu_staff_publication/1037
DOI:
10.1137/090774823
Author(s):
Ng, Michael K.; Weiss, Pierre; Yuan, Xiaoming
Publisher(s):
Society for Industrial & Applied Mathematics (SIAM); Society for Industrial and Applied Mathematics
Tags:
Mathematics; Alternating direction method; Augmented Lagrangian; Image reconstruction; Image restoration; Total-variation
article description
In this paper, we study alternating direction methods for solving constrained totalvariation image restoration and reconstruction problems. Alternating direction methods can be implementable variants of the classical augmented Lagrangian method for optimization problems with separable structures and linear constraints. The proposed framework allows us to solve problems of image restoration, impulse noise removal, inpainting, and image cartoon+texture decomposition. As the constrained model is employed, we need only to input the noise level, and the estimation of the regularization parameter is not required in these imaging problems. Experimental results for such imaging problems are presented to illustrate the effectiveness of the proposed method. We show that the alternating direction method is very efficient for solving image restoration and reconstruction problems. © 2010 Society for Industrial and Applied Mathematics.