Reconstruction of measurable plane sets from their two projections taken in arbitrary directions

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Abstract

The problem of the reconstruction of a measurable plane set from two projections is considered when the directions of the projections are arbitrary. Via a suitable affine transformation, the problem can be reduced to the solved case of orthogonal projections. The result can also be applied for unknown directions. It is proved that merely a knowledge of the projections (i.e. without their directions) is not enough for the unique reconstruction of a set. However, from two given functions it is possible to decide whether they can determine a set from some directions uniquely, and the corresponding directions of the projections are also computable.

Original languageEnglish
Article number010
Pages (from-to)101-107
Number of pages7
JournalInverse Problems
Volume7
Issue number1
DOIs
Publication statusPublished - Dec 1 1991

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics

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