We introduce a function space setting for a class of structural total variation (TV) regularization methods in inverse problems, where the regularizer is defined via a relaxation framework. We show equivalence of the Tikhonov regularization problem to a saddle-point problem where no knowledge of an explicit formulation of the regularization functional is needed. We provide numerical examples, solving the saddle-point problem for weighted-TV denoising and MR-guided PET reconstruction.

This presentation is part of Minisymposium “MS38 - Geometry-driven anisotropic approaches for imaging problems”
organized by: Luca Calatroni (CMAP, École Polytechnique CNRS) , Dario Prandi (CNRS - L2S, CentraleSupélec) , Valentina Franceschi (INRIA Paris) .

Authors:

Kostas Papafitsoros (Weierstrass Institute Berlin)

Martin Holler (École Polytechnique, Université Paris Saclay)

Michael Hintermüller (Humboldt University and Weierstrass Institute Berlin)

Keywords:

image reconstruction, inverse problems, partial differential equation models