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Inversion of circular averages and application of backprojection methods to radar imaging
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
1993 (English)Licentiate thesis, monograph (Other academic)
Abstract [en]

In this report we study two mathematical inverse problems concerning the determination of a function from spherical averages, which appear in certain radar applications. The first inverse problem consists of determining a function from its spherical averages over all circles with center on a straight line and with arbitrary radius. In the second we have averages over discs instead of circles. We define the corresponding operators and their duals, called backprojection operators. We: investigate the properties of these operators and also for which functions the resulting inversion formulas are valid. The inversion formula for the first problem can be expressed by the aid of a backprojection operator. This is used in order to obtain 8n approximate inversion formula for a perturbed problem where we know the averages over circles with center on a smooth curve deviating from the straight line. We describe the qualitative behaviour of this approximative inversion formula contra the original one. Finally we present some numerical results obtained using a simulation program.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet , 1993. , p. 57
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 408
Keywords [en]
inverse problem, backprojection, tomography, integral geometry
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-145876Local ID: LiU-TEK-LIC-1993:50ISBN: 9178711940 (print)OAI: oai:DiVA.org:liu-145876DiVA, id: diva2:1201247
Available from: 2018-04-25 Created: 2018-04-25 Last updated: 2018-12-04Bibliographically approved

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CiteExportLink to record
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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
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  • Other style
More styles
Language
  • de-DE
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  • en-US
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  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf