Bilevel approaches for learning of variational imaging models
This work addresses the problem of improving variational imaging models for researchers and practitioners in computational imaging, but it is incremental as it reviews and extends existing bilevel optimization techniques.
The paper reviews bilevel optimization approaches for learning variational imaging models, focusing on analytical results like existence of minimizers and optimality conditions, and develops Newton-type methods combined with sampling for large databases, with extensive computational verification across various regularizers, noise models, and image datasets.
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.