Analytic reconstruction algorithms in emission tomography with variable attenuation

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2 Citations (Scopus)

Abstract

We present, two analytic reconstruction algorithms applicable in emission tomography with variable attenuation. One of this algorithms is based on the recently discovered explicit inversion formula for the attenuated Radon transform with non-uniform attenuation; it is intended for applications in single-photon emission computed tomography. The second of the methods we present is applicable for approximate inversion of the generalized Radon transform with more general weights for which inversion formulae are not known; inversion of such transforms are required, for instance, in the emission tomography of gases. The latter algorithm is based on an approximate (up to a smoothing term) inversion of the underlying integral operator; in spite of its approximate nature it yields quite accurate reconstructions and exhibits very low sensitivity to noise in data. In fact, when applied to data containing significant level of noise the latter algorithm yields better reconstructions than the first of our mehods (based on theoretically exact inversion formula). We support conclusions of the paper by a number of convincing numerical results.

Original languageEnglish (US)
Pages (from-to)267-286
Number of pages20
JournalJournal of Computational Methods in Sciences and Engineering
Volume1
Issue number2-3
DOIs
StatePublished - 2001

Fingerprint

Inversion Formula
Reconstruction Algorithm
Tomography
Attenuation
Inversion
Radon Transform
Radon
Computed Tomography
Single photon emission computed tomography
Integral Operator
Smoothing
Explicit Formula
Photon
Transform
Numerical Results
Term
Gases

Keywords

  • analytic algorithm
  • Novikov inversion formula
  • Pseudo-differential operator
  • Radon transform
  • SPECT

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mathematics
  • Engineering(all)

Cite this

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title = "Analytic reconstruction algorithms in emission tomography with variable attenuation",
abstract = "We present, two analytic reconstruction algorithms applicable in emission tomography with variable attenuation. One of this algorithms is based on the recently discovered explicit inversion formula for the attenuated Radon transform with non-uniform attenuation; it is intended for applications in single-photon emission computed tomography. The second of the methods we present is applicable for approximate inversion of the generalized Radon transform with more general weights for which inversion formulae are not known; inversion of such transforms are required, for instance, in the emission tomography of gases. The latter algorithm is based on an approximate (up to a smoothing term) inversion of the underlying integral operator; in spite of its approximate nature it yields quite accurate reconstructions and exhibits very low sensitivity to noise in data. In fact, when applied to data containing significant level of noise the latter algorithm yields better reconstructions than the first of our mehods (based on theoretically exact inversion formula). We support conclusions of the paper by a number of convincing numerical results.",
keywords = "analytic algorithm, Novikov inversion formula, Pseudo-differential operator, Radon transform, SPECT",
author = "Leonid Kunyansky",
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AB - We present, two analytic reconstruction algorithms applicable in emission tomography with variable attenuation. One of this algorithms is based on the recently discovered explicit inversion formula for the attenuated Radon transform with non-uniform attenuation; it is intended for applications in single-photon emission computed tomography. The second of the methods we present is applicable for approximate inversion of the generalized Radon transform with more general weights for which inversion formulae are not known; inversion of such transforms are required, for instance, in the emission tomography of gases. The latter algorithm is based on an approximate (up to a smoothing term) inversion of the underlying integral operator; in spite of its approximate nature it yields quite accurate reconstructions and exhibits very low sensitivity to noise in data. In fact, when applied to data containing significant level of noise the latter algorithm yields better reconstructions than the first of our mehods (based on theoretically exact inversion formula). We support conclusions of the paper by a number of convincing numerical results.

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