# A Convex Formulation for Binary Tomography

arXiv: https://arxiv.org/abs/1807.09196 · HTML: https://mlsanity.com/paper/1807.09196/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2018.

## Built on by (most cited first, 2 of 2)

- [Discrete Optimization of Min-Max Violation and its Applications Across Computational Sciences](https://mlsanity.com/paper/2508.13437/) (2025)
- [Supervised Reconstruction for Silhouette Tomography](https://mlsanity.com/paper/2402.07298/) (2024)

## Abstract (arXiv)

Binary tomography is concerned with the recovery of binary images from a few of their projections (i.e., sums of the pixel values along various directions). To reconstruct an image from noisy projection data, one can pose it as a constrained least-squares problem. As the constraints are non-convex, many approaches for solving it rely on either relaxing the constraints or heuristics. In this paper we propose a novel convex formulation, based on the Lagrange dual of the constrained least-squares problem. The resulting problem is a generalized LASSO problem which can be solved efficiently. It is a relaxation in the sense that it can only be guaranteed to give a feasible solution; not necessarily the optimal one. In exhaustive experiments on small images (2x2, 3x3, 4x4) we find, however, that if the problem has a unique solution, our dual approach finds it. In case of multiple solutions, our approach finds the commonalities between the solutions. Further experiments on realistic numerical phantoms and an experiment on X-ray dataset show that our method compares favourably to Total Variation and DART.