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Volume 2, Issue 4
A Compound Algorithm of Denoising Using Second-Order and Fourth-Order Partial Differential Equations

Qianshun Chang, Xuecheng Tai & Lily Xing

DOI: 10.4208/nmtma.2009.m9001s

Numer. Math. Theor. Meth. Appl., 2 (2009), pp. 353-376.

Published online: 2009-02

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  • Abstract

In this paper, we propose a compound algorithm for the image restoration. The algorithm is a convex combination of the ROF model and the LLT model with a parameter function $\theta$. The numerical experiments demonstrate that our compound algorithm is efficient and preserves the main advantages of the two models. In particular, the errors of the compound algorithm in $L_2$ norm between the exact images and corresponding restored images are the smallest among the three models. For images with strong noises, the restored images of the compound algorithm are the best in the corresponding restored images. The proposed algorithm combines the fixed point method, an improved AMG method and the Krylov acceleration. It is found that the combination of these methods is efficient and robust in the image restoration.

  • Keywords

Algorithm of denoising, image restoration, total variation, second-order functional.

  • AMS Subject Headings

68U10, 65M55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-2-353, author = {Qianshun Chang, Xuecheng Tai and Lily Xing}, title = {A Compound Algorithm of Denoising Using Second-Order and Fourth-Order Partial Differential Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2009}, volume = {2}, number = {4}, pages = {353--376}, abstract = {

In this paper, we propose a compound algorithm for the image restoration. The algorithm is a convex combination of the ROF model and the LLT model with a parameter function $\theta$. The numerical experiments demonstrate that our compound algorithm is efficient and preserves the main advantages of the two models. In particular, the errors of the compound algorithm in $L_2$ norm between the exact images and corresponding restored images are the smallest among the three models. For images with strong noises, the restored images of the compound algorithm are the best in the corresponding restored images. The proposed algorithm combines the fixed point method, an improved AMG method and the Krylov acceleration. It is found that the combination of these methods is efficient and robust in the image restoration.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2009.m9001s}, url = {http://global-sci.org/intro/article_detail/nmtma/6029.html} }
TY - JOUR T1 - A Compound Algorithm of Denoising Using Second-Order and Fourth-Order Partial Differential Equations AU - Qianshun Chang, Xuecheng Tai & Lily Xing JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 353 EP - 376 PY - 2009 DA - 2009/02 SN - 2 DO - http://doi.org/10.4208/nmtma.2009.m9001s UR - https://global-sci.org/intro/article_detail/nmtma/6029.html KW - Algorithm of denoising, image restoration, total variation, second-order functional. AB -

In this paper, we propose a compound algorithm for the image restoration. The algorithm is a convex combination of the ROF model and the LLT model with a parameter function $\theta$. The numerical experiments demonstrate that our compound algorithm is efficient and preserves the main advantages of the two models. In particular, the errors of the compound algorithm in $L_2$ norm between the exact images and corresponding restored images are the smallest among the three models. For images with strong noises, the restored images of the compound algorithm are the best in the corresponding restored images. The proposed algorithm combines the fixed point method, an improved AMG method and the Krylov acceleration. It is found that the combination of these methods is efficient and robust in the image restoration.

Qianshun Chang, Xuecheng Tai and Lily Xing. (2009). A Compound Algorithm of Denoising Using Second-Order and Fourth-Order Partial Differential Equations. Numerical Mathematics: Theory, Methods and Applications. 2 (4). 353-376. doi:10.4208/nmtma.2009.m9001s
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