Year: 2024
Author: Wenli Yang, Zhongyi Huang, Wei Zhu
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2201-m2021-0287
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 2 : pp. 313–336
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Image super-resolution Variational model Augmented Lagrangian methods Tailored finite point method.