2009/06/03 by Stolk, Arjen, Batenburg, K. Joost · 1 citation
#11H71 (Secondary) #94A12 (Primary) #94C10 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.0906.0711
Discrete tomography is concerned with the reconstruction of images that are defined on a discrete set of lattice points from their projections in several directions. The range of values that can be assigned to each lattice point is typically a small discrete set. In this paper we present a framework for studying these problems from an algebraic perspective, based on Ring Theory and Commutative Algebra. A principal advantage of this abstract setting is that a vast body of existing theory becomes accessible for solving Discrete Tomography problems. We provide proofs of several new results on the structure of dependencies between projections, including a discrete analogon of the well-known Helgason-Ludwig consistency conditions from continuous tomography.