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An Alternating Direction Method for Total Variation Denoising

Zhiwei (Tony) Qin (zq2107***at***columbia.edu)
Donald Goldfarb (goldfarb***at***columbia.edu)
Shiqian Ma (maxxa007***at***ima.umn.eduu)

Abstract: 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 \cite{goldstein2009split},which is closely related to it, and demonstrate their competitiveness in computational performance on a set of standard test images.

Keywords: alternating direction method, augmented Lagrangian, split Bregman, total variation denoising, variable splitting

Category 1: Convex and Nonsmooth Optimization

Citation: Appearing in Optimization Methods and Software

Download: [PDF]

Entry Submitted: 08/07/2011
Entry Accepted: 08/07/2011
Entry Last Modified: 08/23/2014

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