A Boosting Procedure for Variational-Based Image Restoration

作     者：Samad Wali Zhifang Liu Chunlin Wu Huibin Chang 

作者机构：School of Mathematical SciencesNankai UniversityTianjinChina School of Mathematical SciencesTianjin Normal UniversityTianjinChina 

出 版 物：《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报（英文版）)

年 卷 期：2018年第11卷第1期

页      面：49-73页

核心收录：

学科分类：0820[工学-石油与天然气工程] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：The work of Dr.C.Wu was supported by National Natural Science Foundation of China(Grant No.11301289 and 11531013) Dr.H.Chang was partially supported by National Natural Science Foundation of China(Nos.11501413 and 51609259) China Scholarship Council(CSC),Young backbone of innovative personnel training program No.043-135205GC37 2017-Outstanding Young Innovation Team Cul-tivation Program No.043-135202TD1703 Innovation Project No.043-135202XC1605 of Tianjin Normal University,and the Research Program of China Institute of Water Resources and Hydropower Research(Nos.JZ0145B472016 and JZ0145B862017). 

主　　题：Variational method image restoration total variation boosting augmented Lagrangian method 

摘      要：Variational methods are an important class of methods for general image restoration.Boosting technique has been shown capable of improving many image denoising algorithms.This paper discusses a boosting technique for general variation-al image restoration methods.It broadens the applications of boosting techniques to a wide range of image restoration problems,including not only denoising but also deblur-ring and inpainting.In particular,we combine the recent SOS technique with dynamic parameter to variational methods.The dynamic regularization parameter is motivated by Meyer’s analysis on the ROF model.In each iteration of the boosting scheme,the variational model is solved by augmented Lagrangian method.The convergence analy-sis of the boosting process is shown in a special case of total variation image denoising with a“diskinput data.We have implemented our boosting technique for several im-age restoration problems such as denoising,inpainting and deblurring.The numerical results demonstrate promising improvement over standard variational restoration mod-els such as total variation based models and higher order variational model as total generalized variation.