Stability in discrete tomography: Linear programming, additivity and convexity

Abstract

The problem of reconstructing finite subsets of the integer lattice from X-rays has been studied in discrete mathematics and applied in several fields like image processing, data security, electron microscopy. In this paper we focus on the stability of the reconstruction problem for some lattice sets. First we show some theoretical bounds for additive sets, and a numerical experiment is made by using linear programming to deal with stability for convex sets. © Springer-Verlag Berlin Heidelberg 2003.