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Title
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An algebraic framework for discrete tomography: revealing the structure of dependencies
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Author
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Abstract
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| 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. |
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Language
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English
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Source (journal)
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SIAM journal on discrete mathematics / Society for Industrial and Applied Mathematics [Philadelphia, Pa] - Philadelphia, Pa
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Publication
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Philadelphia, Pa
:
2010
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ISSN
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0895-4801
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DOI
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10.1137/090766693
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Volume/pages
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24
:3
(2010)
, p. 1056-1079
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ISI
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000282291600024
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Full text (Publisher's DOI)
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