Learning optimal spatially-dependent regularization parameters in total variation image denoising

被引：20
|
作者：
Van Chung, Cao [1 ,3 ]
De los Reyes, J. C. [1 ]
Schonlieb, C. B. [2 ]
机构：
[1] Escuela Politec Nacl, Res Ctr Math Modelling MODEMAT, Quito, Ecuador
[2] Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge, England
[3] Hanoi Univ Sci, Ctr High Performance Comp, Hanoi, Vietnam
来源：
INVERSE PROBLEMS | 2017年 / 33卷 / 07期
基金：
英国工程与自然科学研究理事会;
关键词：
optimization-based learning in imaging; bilevel optimization; PDE-constrained optimization; semismooth Newton method; Schwarz domain decomposition method; OPTIMIZATION; SELECTION;
D O I：
10.1088/1361-6420/33/7/074005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a bilevel optimization approach in function space for the choice of spatially dependent regularization parameters in TV image denoising models. First- and second-order optimality conditions for the bilevel problem are studied when the spatially-dependent parameter belongs to the Sobolev space H-1(Omega). A combined Schwarz domain decomposition-semismooth Newton method is proposed for the solution of the full optimality system and local superlinear convergence of the semismooth Newton method is verified. Exhaustive numerical computations are finally carried out to show the suitability of the approach.
引用
收藏
页数：31
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