Published in

IOP Publishing, Inverse Problems, 3(29), p. 035003

DOI: 10.1088/0266-5611/29/3/035003

Links

Tools

Export citation

Search in Google Scholar

Belief Propagation Reconstruction for Discrete Tomography

Journal article published in 2013 by Emmanuelle Gouillart, Florent Krzakala ORCID, Marc Mézard, Lenka Zdeborová
This paper is available in a repository.
This paper is available in a repository.

Full text: Download

Red circle
Preprint: archiving forbidden
Red circle
Postprint: archiving forbidden
Red circle
Published version: archiving forbidden
Policy details
Data provided by SHERPA/RoMEO

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.