Inversion of weighted Radon transforms via finite Fourier series weight approximations

J. P. Guillement; R. G. Novikov

doi:10.1080/17415977.2013.823417

Inversion of weighted Radon transforms via finite Fourier series weight approximations

J. P. Guillement
, R. G. Novikov

Université de Nantes
IEPT RAS

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We consider weighted Radon transforms on the plane. We show that the Chang approximate inversion formula for these transforms admits a significant extension as inversion via finite Fourier series weight approximations. We illustrate this inversion approach by numerical examples for the case of the attenuated Radon transforms in the framework of the single-photon emission computed tomography (SPECT).

langue originale	Anglais
Pages (de - à)	787-802
Nombre de pages	16
journal	Inverse Problems in Science and Engineering
Volume	22
Numéro de publication	5
Les DOIs	https://doi.org/10.1080/17415977.2013.823417
état	Publié - 1 janv. 2014

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10.1080/17415977.2013.823417

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title = "Inversion of weighted Radon transforms via finite Fourier series weight approximations",

abstract = "We consider weighted Radon transforms on the plane. We show that the Chang approximate inversion formula for these transforms admits a significant extension as inversion via finite Fourier series weight approximations. We illustrate this inversion approach by numerical examples for the case of the attenuated Radon transforms in the framework of the single-photon emission computed tomography (SPECT).",

keywords = "Chang's formula, approximate inversion algorithms, emission tomography, finite Fourier series weight approximations, weighted radon transforms",

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year = "2014",

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AU - Novikov, R. G.

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N2 - We consider weighted Radon transforms on the plane. We show that the Chang approximate inversion formula for these transforms admits a significant extension as inversion via finite Fourier series weight approximations. We illustrate this inversion approach by numerical examples for the case of the attenuated Radon transforms in the framework of the single-photon emission computed tomography (SPECT).

AB - We consider weighted Radon transforms on the plane. We show that the Chang approximate inversion formula for these transforms admits a significant extension as inversion via finite Fourier series weight approximations. We illustrate this inversion approach by numerical examples for the case of the attenuated Radon transforms in the framework of the single-photon emission computed tomography (SPECT).

KW - Chang's formula

KW - approximate inversion algorithms

KW - emission tomography

KW - finite Fourier series weight approximations

KW - weighted radon transforms

UR - https://www.scopus.com/pages/publications/84901592513

U2 - 10.1080/17415977.2013.823417

DO - 10.1080/17415977.2013.823417

M3 - Article

AN - SCOPUS:84901592513

SN - 1741-5977

VL - 22

SP - 787

EP - 802

JO - Inverse Problems in Science and Engineering

JF - Inverse Problems in Science and Engineering

IS - 5

ER -

Inversion of weighted Radon transforms via finite Fourier series weight approximations

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