Volume 8, Issue 5
Alternating Minimization Method for Total Variation Based Wavelet Shrinkage Model

Tieyong Zeng, Xiaolong Li & Michael Ng

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

Published online: 2010-08

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  • 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.

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@Article{CiCP-8-976, author = {}, title = {Alternating Minimization Method for Total Variation Based Wavelet Shrinkage Model}, journal = {Communications in Computational Physics}, year = {2010}, volume = {8}, number = {5}, pages = {976--994}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.210709.180310a}, url = {http://global-sci.org/intro/article_detail/cicp/7605.html} }
TY - JOUR T1 - Alternating Minimization Method for Total Variation Based Wavelet Shrinkage Model JO - Communications in Computational Physics VL - 5 SP - 976 EP - 994 PY - 2010 DA - 2010/08 SN - 8 DO - http://doi.org/10.4208/cicp.210709.180310a UR - https://global-sci.org/intro/article_detail/cicp/7605.html KW - AB -

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.

Tieyong Zeng, Xiaolong Li & Michael Ng. (2020). Alternating Minimization Method for Total Variation Based Wavelet Shrinkage Model. Communications in Computational Physics. 8 (5). 976-994. doi:10.4208/cicp.210709.180310a
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