Multi-parameter Tikhonov Regularization—An Augmented Approach  

作　　者：Kazufumi ITO Bangti JIN Tomoya TAKEUCHI 

机构地区：[1]Center for Research in Scientific Computation & Department of Mathematics, North Carolina State University [2]Department of Mathematics, University of California, Riverside, 900 University Ave.Riverside, CA92521, USA. [3]Collaborative Research Center for Innovative Mathematical Modelling, Institute of Industrial Science,The University of Tokyo 4-6-1-Cw601 Komaba, Meguro-ku Tokyo 153-8505, Japan.

出　　处：《Chinese Annals of Mathematics,Series B》2014年第3期383-398,共16页数学年刊（B辑英文版）

基　　金：supported by the Army Research Office under DAAD19-02-1-0394,US-ARO grant 49308MA and US-AFSOR grant FA9550-06-1-0241

摘　　要：We study multi-parameter regularization(multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters from the viewpoint of augmented Tikhonov regularization, and derive a new parameter choice strategy called the balanced discrepancy principle. A priori and a posteriori error estimates are provided to theoretically justify the principles, and numerical algorithms for efficiently implementing the principles are also provided. Numerical results on deblurring are presented to illustrate the feasibility of the balanced discrepancy principle.

关 键 词：Multi-parameter regularization Augmented Tikhonov regularization Balanced discrepancy principle 

分 类 号：O241.8[理学—计算数学]