A Novel Convex Relaxation for Non-Binary Discrete Tomography
Abstract
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.
Cite
@article{arxiv.1703.03769,
title = {A Novel Convex Relaxation for Non-Binary Discrete Tomography},
author = {Jan Kuske and Paul Swoboda and Stefania Petra},
journal= {arXiv preprint arXiv:1703.03769},
year = {2018}
}