Reconstruction of measurable sets from two generalized projections

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...

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Bibliographic Details
Published inElectronic notes in discrete mathematics Vol. 20; pp. 47 - 66
Main Authors Zopf, Steffen, Kuba, Attila
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.07.2005
Subjects
absorption
Discrete tomography
emission discrete tomography
Lorentz' theorem
projection
switching component
Discrete tomography
Lorentz' theorem
projection
absorption
switching component
emission discrete tomography
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Summary: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.
ISSN:1571-0653
1571-0653
DOI:10.1016/j.endm.2005.04.003