Reconstruction of discrete sets with absorption

Attila Kuba, Maurice Nivat

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

The uniqueness problem is considered when binary matrices are to be reconstructed from their absorbed row and column sums. Let the absorption coefficient μ be selected such that eμ=(1+5)/2. Then it is proved that if a binary matrix is non-uniquely determined, then it contains a special pattern of 0s and 1s called composition of alternatively corner-connected components. In a previous paper [Discrete Appl. Math. (submitted)] we proved that this condition is also sufficient, i.e., the existence of such a pattern in the binary matrix is necessary and sufficient for its non-uniqueness.

Original languageEnglish
Pages (from-to)171-194
Number of pages24
JournalLinear Algebra and Its Applications
Volume339
Issue number1-3
DOIs
Publication statusPublished - Dec 15 2001

Keywords

  • Discrete tomography
  • Projections with absorption
  • Reconstruction

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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