Reconstruction of measurable sets from two generalized projections

Steffen Zopf, A. Kuba

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The problem of reconstructing a measurable plane set from its two generalized projections is considered. It means that the projections contain also the effect of a known modification given in the whole plane. This is a more general case than that of a constant absorption within a given material. Via a suitable mapping, this generalized problem can be transformed into the solved case of the classical (non-absorbed and non-generalized) projections, giving a theorem about the characterization of unique, non-unique, and inconsistent projections analogous to Lorentz' theorem. The connection between uniqueness and the existence of so-called generalized switching components is discussed.

Original languageEnglish
Pages (from-to)47-66
Number of pages20
JournalElectronic Notes in Discrete Mathematics
Volume20
DOIs
Publication statusPublished - Jul 1 2005

Fingerprint

Generalized Projection
Measurable set
Projection
Theorem
Inconsistent
Absorption
Uniqueness

Keywords

  • absorption
  • Discrete tomography
  • emission discrete tomography
  • Lorentz' theorem
  • projection
  • switching component

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Reconstruction of measurable sets from two generalized projections. / Zopf, Steffen; Kuba, A.

In: Electronic Notes in Discrete Mathematics, Vol. 20, 01.07.2005, p. 47-66.

Research output: Contribution to journalArticle

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