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Volume 24, Issue 4
An Efficient Tailored Finite Point Method for Rician Denoising and Deblurring

Wenli Yang, Zhongyi Huang & Wei Zhu

DOI: 10.4208/cicp.2018.hh80.03

Commun. Comput. Phys., 24 (2018), pp. 1169-1195.

Published online: 2018-06

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  • Abstract

In this paper, we propose using the tailored-finite-point method (TFPM) to solve the resulting parabolic or elliptic equations when minimizing the Rician denoising model developed by Getreuer et al. in [10] using augmented Lagrangian methods (ALM). Different from traditional finite difference schemes, TFPM employs the method of weighted residuals with collocation technique, which helps get more accurate approximate solutions to the equations and thus reserve more details in restored images. Numerical experiments demonstrate that with the new schemes the quality of restored images has been improved. Besides these, the existence of the minimizer of the Rician denoising model have also been established in this paper.

  • Keywords

Rician denoising, deblurring, variational model, augmented Lagrangian methods, tailored finite point method.

  • AMS Subject Headings

65M32, 68U10, 65K10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-24-1169, author = {}, title = {An Efficient Tailored Finite Point Method for Rician Denoising and Deblurring}, journal = {Communications in Computational Physics}, year = {2018}, volume = {24}, number = {4}, pages = {1169--1195}, abstract = {

In this paper, we propose using the tailored-finite-point method (TFPM) to solve the resulting parabolic or elliptic equations when minimizing the Rician denoising model developed by Getreuer et al. in [10] using augmented Lagrangian methods (ALM). Different from traditional finite difference schemes, TFPM employs the method of weighted residuals with collocation technique, which helps get more accurate approximate solutions to the equations and thus reserve more details in restored images. Numerical experiments demonstrate that with the new schemes the quality of restored images has been improved. Besides these, the existence of the minimizer of the Rician denoising model have also been established in this paper.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2018.hh80.03}, url = {http://global-sci.org/intro/article_detail/cicp/12332.html} }
TY - JOUR T1 - An Efficient Tailored Finite Point Method for Rician Denoising and Deblurring JO - Communications in Computational Physics VL - 4 SP - 1169 EP - 1195 PY - 2018 DA - 2018/06 SN - 24 DO - http://doi.org/10.4208/cicp.2018.hh80.03 UR - https://global-sci.org/intro/article_detail/cicp/12332.html KW - Rician denoising, deblurring, variational model, augmented Lagrangian methods, tailored finite point method. AB -

In this paper, we propose using the tailored-finite-point method (TFPM) to solve the resulting parabolic or elliptic equations when minimizing the Rician denoising model developed by Getreuer et al. in [10] using augmented Lagrangian methods (ALM). Different from traditional finite difference schemes, TFPM employs the method of weighted residuals with collocation technique, which helps get more accurate approximate solutions to the equations and thus reserve more details in restored images. Numerical experiments demonstrate that with the new schemes the quality of restored images has been improved. Besides these, the existence of the minimizer of the Rician denoising model have also been established in this paper.

Wenli Yang, Zhongyi Huang & Wei Zhu. (2020). An Efficient Tailored Finite Point Method for Rician Denoising and Deblurring. Communications in Computational Physics. 24 (4). 1169-1195. doi:10.4208/cicp.2018.hh80.03
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