Exact inversion of the conical Radon transform with a fixed opening angle

We study a new class of Radon transforms defined on circular cones called the conical Radon transform. In it maps a function to its surface integrals over circular cones, and in it maps a function to its integrals along two rays with a common vertex. Such transforms appear in various mathematical mo...

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Bibliographic Details
Published in:Inverse problems 2014-04, Vol.30 (4), p.45007-12
Main Authors: Gouia-Zarrad, Rim, Ambartsoumian, Gaik
Format: Article
Language:English
Subjects:
broken-ray transform
Circular cones
Computational efficiency
conical Radon transform
image reconstruction
integral geometry
Integrals
Inversions
Mathematical analysis
Mathematical models
Radon
Transforms
V-line transform
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Summary:We study a new class of Radon transforms defined on circular cones called the conical Radon transform. In it maps a function to its surface integrals over circular cones, and in it maps a function to its integrals along two rays with a common vertex. Such transforms appear in various mathematical models arising in medical imaging, nuclear industry and homeland security. This paper contains new results about inversion of conical Radon transform with fixed opening angle and vertical central axis in and . New simple explicit inversion formulae are presented in these cases. Numerical simulations were performed to demonstrate the efficiency of the suggested algorithm in 2D.
ISSN:0266-5611
1361-6420
DOI:10.1088/0266-5611/30/4/045007