Considering the question: how non-linear may a non-linear operator be in order to extend the linear regularization theory, we introduce the class of dilinear and diconvex mappings. Using tensorial liftings, we generalize the concept of subgradients and Bregman distances from convex analysis to establish convergence rates under similar assumptions than in the linear setting. Finally, we apply our results to the deautoconvolution problem to derive satisfiable source conditions and numerically provable convergence rates.

This presentation is part of Minisymposium “MS25 - Bilinear and quadratric problems in imaging”
organized by: Felix Krahmer (Technical University of Munich, Department of Mathematics) , Kristian Bredies (Universität Graz) .

Authors:

Robert Beinert (University of Graz)

Keywords:

inverse problems