Belief Propagation Reconstruction for Discrete Tomography

TL;DR

This paper introduces a belief propagation algorithm for reconstructing binary images from tomographic data, outperforming convex optimization methods in efficiency and accuracy, especially with noisy measurements.

Contribution

The paper presents a novel fast message-passing belief propagation algorithm tailored for discrete tomography, specifically binary images, demonstrating improved performance over traditional convex methods.

Findings

Belief propagation outperforms convex optimization in reconstruction quality.

The algorithm is more efficient in terms of computational speed.

Reconstruction accuracy improves with increased number of projections.

Abstract

We consider the reconstruction of a two-dimensional discrete image from a set of tomographic measurements corresponding to the Radon projection. Assuming that the image has a structure where neighbouring pixels have a larger probability to take the same value, we follow a Bayesian approach and introduce a fast message-passing reconstruction algorithm based on belief propagation. For numerical results, we specialize to the case of binary tomography. We test the algorithm on binary synthetic images with different length scales and compare our results against a more usual convex optimization approach. We investigate the reconstruction error as a function of the number of tomographic measurements, corresponding to the number of projection angles. The belief propagation algorithm turns out to be more efficient than the convex-optimization algorithm, both in terms of recovery bounds for noise-free projections, and in terms of reconstruction quality when moderate Gaussian noise is added to the projections.