Inversion of Euler integral transforms with applications to sensor data

Yuliy Baryshnikov, Robert Ghrist, David Lipsky

Research output: Contribution to journalArticle

Abstract

Following the pioneering work of Schapira, we consider topological Radontype integral transforms on constructible Z-valued functions using the Euler characteristic as a measure. Contributions include: (1) application of the Schapira inversion formula to target localization and classification problems in sensor networks; (2) extension and application of the inversion formula to weighted Radon transforms; and (3) pseudo-inversion formulae for inverting annuli (sets of Euler measure zero).

Original languageEnglish (US)
Article number124001
JournalInverse Problems
Volume27
Issue number12
DOIs
StatePublished - Dec 1 2011

ASJC Scopus subject areas

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

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