We present a novel convex relaxation and a corresponding inference algorithm for the non-binary discrete tomography problem, that is, reconstructing discrete-valued images from few linear measurements. In contrast to state of the art approaches that split the problem into a continuous reconstruction problem for the linear measurement constraints and a discrete labeling problem to enforce discrete-valued reconstructions, we propose a joint formulation that addresses both problems simultaneously, resulting in a tighter convex relaxation. For this purpose a constrained graphical model is set up and evaluated using a novel relaxation optimized by dual decomposition. We evaluate our approach experimentally and show superior solutions both mathematically (tighter relaxation) and experimentally in comparison to previously proposed relaxations.

This presentation is part of Minisymposium “MS33 - Advances in reconstruction algorithms for computed tomography (4 parts)”
organized by: Gunay Dogan (Theiss Research, NIST) , Harbir Antil (George Mason University) , Elena Loli Piccolomini (Dept. Computer Science and Engineering, University of Bologna) , Samuli Siltanen (University of Helsinki) .

Authors:

Stefania Petra (University of Heidelberg)

Jan Kuske (Heidelberg University)

Paul Sowoboda (Institute of Science and Technology (IST) Austria, Klosterneuburg)

Keywords:

computed tomography