Generalized and attenuated radon transforms

Restorative approach to the numerical inversion

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

The problem of the function reconstruction on its line integrals with known weight function is considered. The approach studied consists of treating the attenuated projections by the radon transform inversion formula and considering the result of the inversion as a distorted image. A helpful formula describing the distortion is obtained. The norm of the distortion operator is estimated and several iterative restoration algorithms based on the integral transfers are investigated. The results of the numerical inversion of the attenuated radon transform are presented to demonstrate the features of the algorithms.

Original languageEnglish (US)
Article number008
Pages (from-to)809-819
Number of pages11
JournalInverse Problems
Volume8
Issue number5
DOIs
StatePublished - 1992
Externally publishedYes

Fingerprint

Numerical Inversion
Radon Transform
Radon
radon
inversions
Inversion Formula
Curvilinear integral
Restoration
Weight Function
Mathematical operators
Inversion
Projection
Norm
norms
restoration
Operator
projection
Demonstrate
operators

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

Generalized and attenuated radon transforms : Restorative approach to the numerical inversion. / Kunyansky, Leonid.

In: Inverse Problems, Vol. 8, No. 5, 008, 1992, p. 809-819.

Research output: Contribution to journalArticle

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