2016/03/30 by C. Chung, Cao Van Chung, Chung, C. +6 · 9 citations
Computer Science · Engineering · Mathematics · #Algorithm #Applied mathematics #Artificial intelligence #Bilevel optimization #Computation #Computer science #Convergence (economics) #Image (mathematics) #Image and Signal Denoising Methods #Image processing #Image restoration #Mathematical analysis #Mathematical optimization #Mathematics #Newton's method #Nonlinear system #Numerical methods in inverse problems #Optimization problem #Physics #Regularization (linguistics) #Sobolev space #Sparse and Compressive Sensing Techniques #Total variation denoising #math.OC #msc:47N40 #msc:65D18 #msc:65M55 #msc:65N06 #msc:68W10
paper · pdf · doi:10.48550/arxiv.1603.09155
published in arXiv (Cornell University) (Cornell University)
arxiv created 2016/10/16 · arxiv updated 2016/10/18
We consider a bilevel optimization approach in function space for the choice of spatially dependent regularization parameters in TV image restoration models. First- and second-order optimality conditions for the bilevel problem are studied, when the spatially-dependent parameter belongs to the Sobolev space H1(Ω). 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 analyzed. Exhaustive numerical computations are finally carried out to show the suitability of the approach.