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Reconstruction of two‐valued matrices from their two projections
Author(s) -
Kemperman J. H. B.,
Kuba A.
Publication year - 1998
Publication title -
international journal of imaging systems and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.359
H-Index - 47
eISSN - 1098-1098
pISSN - 0899-9457
DOI - 10.1002/(sici)1098-1098(1998)9:2/3<110::aid-ima7>3.0.co;2-e
Subject(s) - uniqueness , mathematics , value (mathematics) , matrix (chemical analysis) , constant (computer programming) , column (typography) , combinatorics , computer science , mathematical analysis , statistics , geometry , connection (principal bundle) , materials science , composite material , programming language
A matrix is said to be two‐valued if its elements assume at most two different values. We studied the problem of reconstructing a two‐valued matrix from its marginals—that is, from its row sums and column sums—but without any knowledge of the value pair on hand. Provided at least one of these marginals is nonconstant, only finitely many (though possibly many) value pairs can lead to a valid reconstruction. Our considerations lead to an efficient algorithm for calculating all possible solutions, each with its own value pair. Special attention is given to uniqueness pairs—that is, value pairs to which there corresponds precisely one matrix having the correct marginals. Unless both marginals are constant, there can be no more than two uniqueness pairs. © 1998 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 9, 110–117, 1998