Bilevel approaches for learning of variational imaging models

2015/05/08 by Luca Calatroni, Cao Chung, Calatroni, Luca +10 · 6 citations
Computer Science · Engineering · Mathematics · Medicine · #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Medical Image Segmentation Techniques #Medical Imaging Techniques and Applications #Optimization and Control (math.OC) #Reservoir Engineering and Simulation Methods #cs.CV #math.OC

paper · pdf · doi:10.48550/arxiv.1505.02120

arxiv created 2015/05/08 · openalex publication_date 2015/05/08 · arxiv updated 2016/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We review some recent learning approaches in variational imaging, based on bilevel optimisation, and emphasize the importance of their treatment in function space. The paper covers both analytical and numerical techniques. Analytically, we include results on the existence and structure of minimisers, as well as optimality conditions for their characterisation. Based on this information, Newton type methods are studied for the solution of the problems at hand, combining them with sampling techniques in case of large databases. The computational verification of the developed techniques is extensively documented, covering instances with different type of regularisers, several noise models, spatially dependent weights and large image databases.

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