Kristian Bredies

Kristian Bredies, Tuomo Valkonen

Total Generalized Variation (TGV) has recently been introduced as penalty functional for modelling images with edges as well as smooth variations. It can be interpreted as a "sparse" penalization of optimal balancing from the first up to the $k$-th distributional derivative and leads to desirable results when applied to image denoising, i.e., $L^2$-fitting with TGV penalty. The present paper studies TGV of second order in the context of solving ill-posed linear inverse problems. Existence and stability for solutions of Tikhonov-functional minimization with respect to the data is shown and applied to the problem of recovering an image from blurred and noisy data.

Clemens Schiffer, Kristian Bredies

A new method for reducing metal artifacts in X-ray computed tomography (CT) images is presented. It bases on the solution of a convex optimization problem with inequality constraints on the sinogram, and total variation regularization for the reconstructed image. The Chambolle-Pock algorithm is used to numerically solve the discretized version of the optimization problem. As proof of concept we present and discuss numerical results for synthetic data.