Commun. Comput. Phys., 8 (2010), pp. 976-994.


Alternating Minimization Method for Total Variation Based Wavelet Shrinkage Model

Tieyong Zeng 1, Xiaolong Li 2, Michael Ng 1*

1 Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China.
2 Institute of Computer Science and Technology, Peking University, Beijing 100871, China.

Received 21 July 2009; Accepted (in revised version) 18 March 2010
Available online 31 May 2010
doi:10.4208/cicp.210709.180310a

Abstract

In this paper, we introduce a novel hybrid variational model which generalizes the classical total variation method and the wavelet shrinkage method. An alternating minimization direction algorithm is then employed. We also prove that it converges strongly to the minimizer of the proposed hybrid model. Finally, some numerical examples illustrate clearly that the new model outperforms the standard total variation method and wavelet shrinkage method as it recovers better image details and avoids the Gibbs oscillations.

AMS subject classifications: 90C25, 52A41, 28E99, 62P35

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Key words: Alternating minimization, convergence, Gibbs oscillation, wavelet shrinkage, total variation.

*Corresponding author.
Email: zeng@hkbu.edu.hk (T. Zeng), lixiaolong@icst.pku.edu.cn (X. Li), mng@math.hkbu.edu.hk (M. Ng)
 

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