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Mathematical Problems in Engineering
Volume 2014, Article ID 157893, 11 pages
Research Article

An Adaptive Total Generalized Variation Model with Augmented Lagrangian Method for Image Denoising

1Unit 302, Xi’an Institute of High-Tech, Xi’an 710025, China
2Unit 303, Xi’an Institute of High-Tech, Xi’an 710025, China

Received 3 March 2014; Revised 20 May 2014; Accepted 25 May 2014; Published 10 July 2014

Academic Editor: Fatih Yaman

Copyright © 2014 Chuan He et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose an adaptive total generalized variation (TGV) based model, aiming at achieving a balance between edge preservation and region smoothness for image denoising. The variable splitting (VS) and the classical augmented Lagrangian method (ALM) are used to solve the proposed model. With the proposed adaptive model and ALM, the regularization parameter, which balances the data fidelity and the regularizer, is refreshed with a closed form in each iterate, and the image denoising can be accomplished without manual interference. Numerical results indicate that our method is effective in staircasing effect suppression and holds superiority over some other state-of-the-art methods both in quantitative and in qualitative assessment.