An alternating direction method for total variation denoising

We consider the image denoising problem using total variation (TV) regularization. This problem can be computationally challenging to solve due to the non-differentiability and non-linearity of the regularization term. We propose an alternating direction augmented Lagrangian (ADAL) method, based on...

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Bibliographic Details
Published in:Optimization methods & software 2015-05, Vol.30 (3), p.594-615
Main Authors: Qin, Zhiwei (Tony), Goldfarb, Donald, Ma, Shiqian
Format: Article
Language:English
Subjects:
alternating direction method
augmented Lagrangian
Computation
Convergence
Lagrange multiplier
Mathematical models
Noise reduction
Optimization
Regularization
split Bregman
Splitting
Television
total variation denoising
variable splitting
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Summary:We consider the image denoising problem using total variation (TV) regularization. This problem can be computationally challenging to solve due to the non-differentiability and non-linearity of the regularization term. We propose an alternating direction augmented Lagrangian (ADAL) method, based on a new variable splitting approach that results in subproblems that can be solved efficiently and exactly. The global convergence of the new algorithm is established for the anisotropic TV model. For the isotropic TV model, by doing further variable splitting, we are able to derive an ADAL method that is globally convergent. We compare our methods with the split Bregman method [T. Goldstein and S. Osher, The split Bregman method for l1-regularized problems, SIAM J. Imaging Sci. 2 (2009), pp. 323],which is closely related to it, and demonstrate their competitiveness in computational performance on a set of standard test images.
ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2014.955100