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

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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).

Original language	English
Pages (from-to)	787-802
Number of pages	16
Journal	Inverse Problems in Science and Engineering
Volume	22
Issue number	5
DOIs	https://doi.org/10.1080/17415977.2013.823417
Publication status	Published - 1 Jan 2014

Keywords

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

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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",

author = "Guillement, \{J. P.\} and Novikov, \{R. G.\}",

year = "2014",

month = jan,

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doi = "10.1080/17415977.2013.823417",

language = "English",

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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

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

Abstract

Keywords

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