Title
An algebraic framework for discrete tomography: revealing the structure of dependencies An algebraic framework for discrete tomography: revealing the structure of dependencies
Author
Faculty/Department
Faculty of Sciences. Physics
Publication type
article
Publication
Philadelphia, Pa ,
Subject
Mathematics
Source (journal)
SIAM journal on discrete mathematics / Society for Industrial and Applied Mathematics [Philadelphia, Pa] - Philadelphia, Pa
Volume/pages
24(2010) :3 , p. 1056-1079
ISSN
0895-4801
ISI
000282291600024
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
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 HelgasonLudwig consistency conditions from continuous tomography.
E-info
http://dx.doi.org/10.1137/090766693
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