2 results
Search Results
Now showing 1 - 2 of 2
- ItemVariable step mollifiers and applications(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Hintermüller, Michael; Papafitsoros, Kostas; Rautenberg, Carlos N.We consider a mollifying operator with variable step that, in contrast to the standard mollification, is able to preserve the boundary values of functions. We prove boundedness of the operator in all basic Lebesgue, Sobolev and BV spaces as well as corresponding approximation results. The results are then applied to extend recently developed theory concerning the density of convex intersections.
- ItemGenerating structured non-smooth priors and associated primal-dual methods(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Hintermüller, Michael; Papafitsoros, KostasThe purpose of the present chapter is to bind together and extend some recent developments regarding data-driven non-smooth regularization techniques in image processing through the means of a bilevel minimization scheme. The scheme, considered in function space, takes advantage of a dualization framework and it is designed to produce spatially varying regularization parameters adapted to the data for well-known regularizers, e.g. Total Variation and Total Generalized variation, leading to automated (monolithic), image reconstruction workflows. An inclusion of the theory of bilevel optimization and the theoretical background of the dualization framework, as well as a brief review of the aforementioned regularizers and their parameterization, makes this chapter a self-contained one. Aspects of the numerical implementation of the scheme are discussed and numerical examples are provided.