# A Novel Convex Relaxation for Non-Binary Discrete Tomography

arXiv: https://arxiv.org/abs/1703.03769 · HTML: https://mlsanity.com/paper/1703.03769/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Mar 2017.

## Built on by (most cited first, 1 of 1)

- [Structured Prediction Problem Archive](https://mlsanity.com/paper/2202.03574/) (2022)

## Abstract (arXiv)

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.