Bounds on the quality of reconstructed images in binary tomography

Authors:
K. Joost Batenburg;Wagner Fortes;Lajos Hajdu;Robert Tijdeman
Affiliations:
Centrum Wiskunde & Informatica, Science Park 123, 1098 XG Amsterdam, The Netherlands and Vision Lab, University of Antwerp, Belgium;Centrum Wiskunde & Informatica, Science Park 123, 1098 XG Amsterdam, The Netherlands and Mathematical Institute, Leiden University, The Netherlands;Institute of Mathematics, University of Debrecen, Hungary and Number Theory Research Group of the Hungarian Academy of Sciences, Debrecen, Hungary;Mathematical Institute, Leiden University, The Netherlands
Venue:
Discrete Applied Mathematics
Year:
2013

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Abstract

Binary tomography deals with the problem of reconstructing a binary image from its projections. In particular, there is a focus on highly underdetermined reconstruction problems for which many solutions may exist. In such cases, it is important to have a quality measure for the reconstruction with respect to the unknown original image. In this article, we derive a series of upper bounds that can be used to guarantee the quality of a reconstructed binary image. The bounds limit the number of pixels that can be incorrect in the reconstructed image with respect to the original image. We provide several versions of these bounds, ranging from bounds on the difference between any two binary solutions of a tomography problem to bounds on the difference between approximate solutions and the original object. The bounds are evaluated experimentally for a range of test images, based on simulated projection data.