English

A Novel Convex Relaxation for Non-Binary Discrete Tomography

Optimization and Control 2018-12-27 v1 Combinatorics

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.

Keywords

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}
}
R2 v1 2026-06-22T18:42:32.123Z