Bounds on the quality of reconstructed images in binary tomography

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.