Paper Info
Title
Stability in discrete tomography: some positive results
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 data security, electron microscopy, and medical imaging. In this paper, we focus on the stability of the reconstruction problem for some special lattice sets. First we prove that if the sets are additive, then a stability result holds for very small errors. Then, we study the stability of reconstructing convex sets from both an experimental and a theoretical point of view. Numerical experiments are conducted by using linear programming and they support the conjecture that convex sets are additive with respect to a set of suitable directions. Consequently, the reconstruction problem is stable. The theoretical investigation provides a stability result for convex lattice sets. This result permits to address the problem proposed by Hammer (in: Convexity, vol. VII, Proceedings of the Symposia in Pure Mathematics, American Mathematical Society, Providence, RI, 1963, pp. 498-499).
Year
DOI
Venue
2005
10.1016/j.dam.2004.09.012
Discrete Applied Mathematics
Keywords
Field
DocType
reconstruction problem,discrete tomography,theoretical investigation,pure mathematics,linear programming,theoretical point,positive result,stability result,stability,convex set,american mathematical society,integer lattice,special lattice set,convexity,additivity,convex lattice set,data security,discrete mathematics,linear program,electron microscopy
Additive function,Convexity,Combinatorics,Discrete tomography,Convex set,Regular polygon,Linear programming,Integer lattice,Conjecture,Mathematics
Journal
Volume
Issue
ISSN
147
2-3
Discrete Applied Mathematics
Citations 
PageRank 
References 
12
0.89
9
Authors
2
Name
Order
Citations
PageRank
Sara Brunetti112216.23
Alain Daurat211214.08