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Volume 42, Issue 2
Image Super-Resolution Reconstruction by Huber Regularization and Tailored Finite Point Method

Wenli Yang, Zhongyi Huang & Wei Zhu

J. Comp. Math., 42 (2024), pp. 313-336.

Published online: 2024-01

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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 Huber regularization based image super-resolution model using the augmented Lagrangian method (ALM). The Huber regularization based image super-resolution model can ameliorate the staircase for restored images. TFPM employs the method of weighted residuals with collocation technique, which helps get more accurate approximate solutions to the equations and reserve more details in restored images. We compare the new schemes with the Marquina-Osher model, the image super-resolution convolutional neural network (SRCNN) and the classical interpolation methods: bilinear interpolation, nearest-neighbor interpolation and bicubic interpolation. Numerical experiments are presented to demonstrate that with the new schemes the quality of the super-resolution images has been improved. Besides these, the existence of the minimizer of the Huber regularization based image super-resolution model and the convergence of the proposed algorithm are also established in this paper.

  • AMS Subject Headings

65M32, 68U10, 65K10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-42-313, author = {Yang , WenliHuang , Zhongyi and Zhu , Wei}, title = {Image Super-Resolution Reconstruction by Huber Regularization and Tailored Finite Point Method}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {42}, number = {2}, pages = {313--336}, abstract = {

In this paper, we propose using the tailored finite point method (TFPM) to solve the resulting parabolic or elliptic equations when minimizing the Huber regularization based image super-resolution model using the augmented Lagrangian method (ALM). The Huber regularization based image super-resolution model can ameliorate the staircase for restored images. TFPM employs the method of weighted residuals with collocation technique, which helps get more accurate approximate solutions to the equations and reserve more details in restored images. We compare the new schemes with the Marquina-Osher model, the image super-resolution convolutional neural network (SRCNN) and the classical interpolation methods: bilinear interpolation, nearest-neighbor interpolation and bicubic interpolation. Numerical experiments are presented to demonstrate that with the new schemes the quality of the super-resolution images has been improved. Besides these, the existence of the minimizer of the Huber regularization based image super-resolution model and the convergence of the proposed algorithm are also established in this paper.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2201-m2021-0287}, url = {http://global-sci.org/intro/article_detail/jcm/22882.html} }
TY - JOUR T1 - Image Super-Resolution Reconstruction by Huber Regularization and Tailored Finite Point Method AU - Yang , Wenli AU - Huang , Zhongyi AU - Zhu , Wei JO - Journal of Computational Mathematics VL - 2 SP - 313 EP - 336 PY - 2024 DA - 2024/01 SN - 42 DO - http://doi.org/10.4208/jcm.2201-m2021-0287 UR - https://global-sci.org/intro/article_detail/jcm/22882.html KW - Image super-resolution, 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 Huber regularization based image super-resolution model using the augmented Lagrangian method (ALM). The Huber regularization based image super-resolution model can ameliorate the staircase for restored images. TFPM employs the method of weighted residuals with collocation technique, which helps get more accurate approximate solutions to the equations and reserve more details in restored images. We compare the new schemes with the Marquina-Osher model, the image super-resolution convolutional neural network (SRCNN) and the classical interpolation methods: bilinear interpolation, nearest-neighbor interpolation and bicubic interpolation. Numerical experiments are presented to demonstrate that with the new schemes the quality of the super-resolution images has been improved. Besides these, the existence of the minimizer of the Huber regularization based image super-resolution model and the convergence of the proposed algorithm are also established in this paper.

Yang , WenliHuang , Zhongyi and Zhu , Wei. (2024). Image Super-Resolution Reconstruction by Huber Regularization and Tailored Finite Point Method. Journal of Computational Mathematics. 42 (2). 313-336. doi:10.4208/jcm.2201-m2021-0287
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