Bilevel approaches for learning of variational imaging models [article]

Luca Calatroni, Cao Chung, Juan Carlos De Los Reyes, Carola-Bibiane Schönlieb, Tuomo Valkonen
2015 arXiv   pre-print
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
more » ... ues 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.
arXiv:1505.02120v1 fatcat:zbj34jpfsbetxkb2fjc2ef2674