IMAGE SUPER-RESOLUTION RECONSTRUCTION BY HUBER REGULARIZATION AND TAILORED FINITE POINT METHOD

作     者：Wenli Yang Zhongyi Huang Wei Zhu Wenli Yang;Zhongyi Huang;Wei Zhu

作者机构：School of MathematicsChina University of Mining and TechnologyXuzhou 221116China Department of MathematicsTsinghua UniversityBeijing 100084China Department of MathematicsUniversity of AlabamaTuscaloosaAL 35487USA 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2024年第42卷第2期

页      面：313-336页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：partially supported by the NSFC Project Nos.12001529 12025104 11871298 81930119. 

主　　题：Image super-resolution Variational model Augmented Lagrangian methods Tailored finite point method 

摘      要：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 Hu-ber regularization based image super-resolution model can ameliorate the staircase for restored images.TFPM employs the method of weighted residuals with collocation tech-nique,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.