# A Novel Convex Relaxation for Non-Binary Discrete Tomography

## TL;DR

This paper introduces a new convex relaxation method for non-binary discrete tomography that jointly solves reconstruction and labeling, leading to more accurate and tighter solutions than existing approaches.

## Contribution

A novel joint convex relaxation formulation for non-binary discrete tomography that improves solution tightness and integrates reconstruction and labeling tasks.

## Key findings

- Tighter convex relaxation achieved compared to previous methods.
- Experimental results show superior reconstruction quality.
- The approach outperforms existing relaxations both mathematically and empirically.

## 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.