Stability results for uniquely determined sets from two directions in discrete tomography

TL;DR

This paper establishes stability bounds for reconstructing binary images from two projections in discrete tomography, showing how errors in projections affect the uniqueness and size of reconstructions.

Contribution

It provides new stability results linking projection errors to the size and uniqueness of binary image reconstructions in discrete tomography.

Findings

Reconstruction disjointness is limited by image size and projection differences.

An upper bound on image size is derived based on projection error and intersection size.

Reconstruction stability depends on the magnitude of projection errors.

Abstract

In this paper we prove several new stability results for the reconstruction of binary images from two projections. We consider an original image that is uniquely determined by its projections and possible reconstructions from slightly different projections. We show that for a given difference in the projections, the reconstruction can only be disjoint from the original image if the size of the image is not too large. We also prove an upper bound for the size of the image given the error in the projections and the size of the intersection between the image and the reconstruction.