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Volume 15, Issue 1
An Efficient Variational Model for Multiplicative Noise Removal

Min Liu & Xiliang Lu

Numer. Math. Theor. Meth. Appl., 15 (2022), pp. 125-140.

Published online: 2022-02

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  • Abstract

In this paper, an efficient variational model for multiplicative noise removal is proposed. By using a MAP estimator, Aubert and Aujol [SIAM J. Appl. Math., 68(2008), pp. 925-946] derived a nonconvex cost functional. With logarithmic transformation, we transform the image into a logarithmic domain which makes the fidelity convex in the transform domain. Considering the TV regularization term in logarithmic domain may cause oversmoothness numerically, we propose the TV regularization directly in the original image domain, which preserves more details of images. An alternative minimization algorithm is applied to solve the optimization problem. The $z$-subproblem can be solved by a closed formula, which makes the method very efficient. The convergence of the algorithm is discussed. The numerical experiments show the efficiency of the proposed model and algorithm.

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-15-125, author = {Liu , Min and Lu , Xiliang}, title = {An Efficient Variational Model for Multiplicative Noise Removal}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2022}, volume = {15}, number = {1}, pages = {125--140}, abstract = {

In this paper, an efficient variational model for multiplicative noise removal is proposed. By using a MAP estimator, Aubert and Aujol [SIAM J. Appl. Math., 68(2008), pp. 925-946] derived a nonconvex cost functional. With logarithmic transformation, we transform the image into a logarithmic domain which makes the fidelity convex in the transform domain. Considering the TV regularization term in logarithmic domain may cause oversmoothness numerically, we propose the TV regularization directly in the original image domain, which preserves more details of images. An alternative minimization algorithm is applied to solve the optimization problem. The $z$-subproblem can be solved by a closed formula, which makes the method very efficient. The convergence of the algorithm is discussed. The numerical experiments show the efficiency of the proposed model and algorithm.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2021-0065 }, url = {http://global-sci.org/intro/article_detail/nmtma/20224.html} }
TY - JOUR T1 - An Efficient Variational Model for Multiplicative Noise Removal AU - Liu , Min AU - Lu , Xiliang JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 125 EP - 140 PY - 2022 DA - 2022/02 SN - 15 DO - http://doi.org/10.4208/nmtma.OA-2021-0065 UR - https://global-sci.org/intro/article_detail/nmtma/20224.html KW - Multiplicative noise, variational model, alternating direction minimization. AB -

In this paper, an efficient variational model for multiplicative noise removal is proposed. By using a MAP estimator, Aubert and Aujol [SIAM J. Appl. Math., 68(2008), pp. 925-946] derived a nonconvex cost functional. With logarithmic transformation, we transform the image into a logarithmic domain which makes the fidelity convex in the transform domain. Considering the TV regularization term in logarithmic domain may cause oversmoothness numerically, we propose the TV regularization directly in the original image domain, which preserves more details of images. An alternative minimization algorithm is applied to solve the optimization problem. The $z$-subproblem can be solved by a closed formula, which makes the method very efficient. The convergence of the algorithm is discussed. The numerical experiments show the efficiency of the proposed model and algorithm.

Liu , Min and Lu , Xiliang. (2022). An Efficient Variational Model for Multiplicative Noise Removal. Numerical Mathematics: Theory, Methods and Applications. 15 (1). 125-140. doi:10.4208/nmtma.OA-2021-0065
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