Efficient Convex Optimization Approaches to Variational Image Fusion

作     者：Jing Yuan Brandon Miles Greg Garvin Xue-Cheng Tai Aaron Fenster 

作者机构：Medical Imaging LabRobarts Research InstituteUniversity of Western OntarioLondon ONCanada N6A 5B7 Department of Medical ImagingSt Jospeh’s HealthCareLondon ONCanada Department of MathematicsUniversity of BergenBergenNorway 

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：2014年第7卷第2期

页      面：234-250页

核心收录：

学科分类：0820[工学-石油与天然气工程] 08[工学] 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：J.Yuan and A.Fenster gratefully acknowledge funding from the Canadian Institutes of Health Research,and the Ontario Institute of Cancer Research B.Miles gratefully acknowledges funding from the Graduate Program in BioMedical Engineering at the University of Western Ontario and the Computer Assisted Medical Intervention Training Program,which is funded by the Natural Sciences and Engineer-ing Research Council of Canada A.Fenster holds a Canada Research Chair in Biomedi-cal Engineering,and acknowledges the support of the Canada Research Chair Program 

主　　题：Convex optimization primal-dual programming combinatorial optimization totalvariation regularization image fusion 

摘      要：Image fusion is an imaging technique to visualize information from multiple imaging sources in one single image,which is widely used in remote sensing,medical imaging *** this work,we study two variational approaches to image fusion which are closely related to the standard TV-L_(2) and TV-L_(1) image approximation *** investigate their convex optimization formulations,under the perspective of primal and dual,and propose their associated new image decomposition *** addition,we consider the TV-L_(1) based image fusion approach and study the specified problem of fusing two discrete-constrained images f_(1)(x)∈L_(1) and f_(2)(x)∈L_(2),where L_(1) and L_(2) are the sets of linearly-ordered discrete *** prove that the TV-L_(1) based image fusion actually gives rise to the exact convex relaxation to the corresponding nonconvex image fusion constrained by the discretevalued set u(x)∈L_(1)∪L_(2).This extends the results for the global optimization of the discrete-constrained TV-L_(1) image approximation[8,36]to the case of image *** a big numerical advantage of the two proposed dual models,we show both of them directly lead to new fast and reliable algorithms,based on modern convex optimization *** with medical images,remote sensing images and multi-focus images visibly show the qualitative differences between the two studied variational models of image *** also apply the new variational approaches to fusing 3D medical images.