An Analytic Inversion Formula for a Radon Transform on a Class of Cones

C. Tarpau; Javier Cebeiro; Mai K. Nguyen; Geneviève Rollet; Laurent Dumas

doi:10.32523/2306-6172-2022-10-3-73-83

An Analytic Inversion Formula for a Radon Transform on a Class of Cones

C. Tarpau^*, Javier Cebeiro, Mai K. Nguyen, Geneviève Rollet, Laurent Dumas

^*Corresponding author for this work

School of Mathematical & Computer Sciences

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Since the works of Radon and Cormack on the classical Radon transform on straight lines, several generalizations involving integrations on conical surfaces have been studied. In this article, we introduce a new family of conical surfaces with arbitrary vertices of the space and axes through the origin and study the corresponding Radon transform. We derive its analytical inversion in two and three dimensions.

Original language	English
Pages (from-to)	73-83
Number of pages	11
Journal	Eurasian Journal of Mathematical and Computer Applications
Volume	10
Issue number	3
DOIs	https://doi.org/10.32523/2306-6172-2022-10-3-73-83
Publication status	Published - 2022

Keywords

Analytical inversion
Generalized radon transforms
Image reconstruction
Inverse problems

ASJC Scopus subject areas

Information Systems
Modelling and Simulation
Mathematical Physics
Computer Science Applications
Computational Mathematics
Applied Mathematics

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abstract = "Since the works of Radon and Cormack on the classical Radon transform on straight lines, several generalizations involving integrations on conical surfaces have been studied. In this article, we introduce a new family of conical surfaces with arbitrary vertices of the space and axes through the origin and study the corresponding Radon transform. We derive its analytical inversion in two and three dimensions.",

keywords = "Analytical inversion, Generalized radon transforms, Image reconstruction, Inverse problems",

author = "C. Tarpau and Javier Cebeiro and Nguyen, {Mai K.} and Genevi{\`e}ve Rollet and Laurent Dumas",

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AU - Tarpau, C.

AU - Cebeiro, Javier

AU - Nguyen, Mai K.

AU - Rollet, Geneviève

AU - Dumas, Laurent

PY - 2022

Y1 - 2022

N2 - Since the works of Radon and Cormack on the classical Radon transform on straight lines, several generalizations involving integrations on conical surfaces have been studied. In this article, we introduce a new family of conical surfaces with arbitrary vertices of the space and axes through the origin and study the corresponding Radon transform. We derive its analytical inversion in two and three dimensions.

AB - Since the works of Radon and Cormack on the classical Radon transform on straight lines, several generalizations involving integrations on conical surfaces have been studied. In this article, we introduce a new family of conical surfaces with arbitrary vertices of the space and axes through the origin and study the corresponding Radon transform. We derive its analytical inversion in two and three dimensions.

KW - Analytical inversion

KW - Generalized radon transforms

KW - Image reconstruction

KW - Inverse problems

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U2 - 10.32523/2306-6172-2022-10-3-73-83

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M3 - Article

AN - SCOPUS:85139330834

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JO - Eurasian Journal of Mathematical and Computer Applications

JF - Eurasian Journal of Mathematical and Computer Applications

IS - 3

ER -

An Analytic Inversion Formula for a Radon Transform on a Class of Cones

Abstract

Keywords

ASJC Scopus subject areas

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