We propose different versions of the TGV denoising method, which have several advantages over the classical one: Switching from penalties to constraints and changing the variables allows for simple universal parameter choice methods and leads to finite duality gaps. We use the Douglas-Rachford method to solve these variational problems. We solve the large linear subproblems inexactly by the preconditioned conjugate gradient method and develop effective preconditioners.

This presentation is part of Minisymposium “MS13 - Optimization for Imaging and Big Data (2 parts)”
organized by: Margherita Porcelli (University of Firenze) , Francesco Rinaldi (University of Padova) .

Authors:

Lena Vestweber (Technische Universität Braunschweig)

Dirk Lorenz (Technische Universität Braunschweig)

Birgit Komander (Technische Universität Braunschweig)

Keywords:

image reconstruction, nonlinear optimization, numerical linear algebra, variational methods