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Volume 15, Issue 2
New Splitting Algorithms for Multiplicative Noise Removal Based on Aubert-Aujol Model

Yu Gan, Jie Zhang & Huibin Chang

Numer. Math. Theor. Meth. Appl., 15 (2022), pp. 415-441.

Published online: 2022-03

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  • Abstract

In this paper, we propose new algorithms for multiplicative noise removal based on the Aubert-Aujol (AA) model. By introducing a constraint from the forward model with an auxiliary variable for the noise, the NEMA (short for Noise Estimate based Multiplicative noise removal by alternating direction method of multipliers (ADMM)) is firstly given. To further reduce the computational cost, an additional proximal term is considered for the subproblem with regard to the original variable, the NEMA$_f$ (short for a variant of NEMA with fully splitting form) is further proposed. We conduct numerous experiments to show the convergence and performance of the proposed algorithms. Namely, the restoration results by the proposed algorithms are better in terms of SNRs for image deblurring than other compared methods including two popular algorithms for AA model and three algorithms of its convex variants.

  • AMS Subject Headings

15A29, 65K10, 68U10, 94A08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-15-415, author = {Gan , YuZhang , Jie and Chang , Huibin}, title = {New Splitting Algorithms for Multiplicative Noise Removal Based on Aubert-Aujol Model}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2022}, volume = {15}, number = {2}, pages = {415--441}, abstract = {

In this paper, we propose new algorithms for multiplicative noise removal based on the Aubert-Aujol (AA) model. By introducing a constraint from the forward model with an auxiliary variable for the noise, the NEMA (short for Noise Estimate based Multiplicative noise removal by alternating direction method of multipliers (ADMM)) is firstly given. To further reduce the computational cost, an additional proximal term is considered for the subproblem with regard to the original variable, the NEMA$_f$ (short for a variant of NEMA with fully splitting form) is further proposed. We conduct numerous experiments to show the convergence and performance of the proposed algorithms. Namely, the restoration results by the proposed algorithms are better in terms of SNRs for image deblurring than other compared methods including two popular algorithms for AA model and three algorithms of its convex variants.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2021-0134}, url = {http://global-sci.org/intro/article_detail/nmtma/20358.html} }
TY - JOUR T1 - New Splitting Algorithms for Multiplicative Noise Removal Based on Aubert-Aujol Model AU - Gan , Yu AU - Zhang , Jie AU - Chang , Huibin JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 415 EP - 441 PY - 2022 DA - 2022/03 SN - 15 DO - http://doi.org/10.4208/nmtma.OA-2021-0134 UR - https://global-sci.org/intro/article_detail/nmtma/20358.html KW - Alternating direction method of multipliers, image denoising and deblurring, multiplicative noise, total variation. AB -

In this paper, we propose new algorithms for multiplicative noise removal based on the Aubert-Aujol (AA) model. By introducing a constraint from the forward model with an auxiliary variable for the noise, the NEMA (short for Noise Estimate based Multiplicative noise removal by alternating direction method of multipliers (ADMM)) is firstly given. To further reduce the computational cost, an additional proximal term is considered for the subproblem with regard to the original variable, the NEMA$_f$ (short for a variant of NEMA with fully splitting form) is further proposed. We conduct numerous experiments to show the convergence and performance of the proposed algorithms. Namely, the restoration results by the proposed algorithms are better in terms of SNRs for image deblurring than other compared methods including two popular algorithms for AA model and three algorithms of its convex variants.

Yu Gan, Jie Zhang & Huibin Chang. (2022). New Splitting Algorithms for Multiplicative Noise Removal Based on Aubert-Aujol Model. Numerical Mathematics: Theory, Methods and Applications. 15 (2). 415-441. doi:10.4208/nmtma.OA-2021-0134
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