2021/07/16 by Juan Carlos De los Reyes, Reyes, Juan Carlos De los, David Villacís +1
Engineering · Mathematics · Medicine · #49K99 #65K10 #68T99 #68U10 #90C33 #FOS: Mathematics #Medical Imaging Techniques and Applications #Numerical methods in inverse problems #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #math.OC #msc:49K99 #msc:65K10 #msc:68T99 #msc:68U10 #msc:90C33
paper · pdf · doi:10.48550/arxiv.2107.08100
33 pages, 9 figures, 4 tables
arxiv created 2021/07/16 · openalex publication_date 2021/07/16 · arxiv updated 2021/07/20 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We address the problem of optimal scale-dependent parameter learning in total variation image denoising. Such problems are formulated as bilevel optimization instances with total variation denoising problems as lower-level constraints. For the bilevel problem, we are able to derive M-stationarity conditions, after characterizing the corresponding Mordukhovich generalized normal cone and verifying suitable constraint qualification conditions. We also derive B-stationarity conditions, after investigating the Lipschitz continuity and directional differentiability of the lower-level solution operator. A characterization of the Bouligand subdifferential of the solution mapping, by means of a properly defined linear system, is provided as well. Based on this characterization, we propose a two-phase non-smooth trust-region algorithm for the numerical solution of the bilevel problem and test it computationally for two particular experimental settings.