Inversion of the spherical Radon transform on spheres through the origin using the regular Radon transform

Sunghwan  Moon

doi:10.3934/cpaa.2016.15.1029

Article Contents

2016, Volume 15, Issue 3: 1029-1039. Doi: 10.3934/cpaa.2016.15.1029

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Inversion of the spherical Radon transform on spheres through the origin using the regular Radon transform

Sunghwan Moon^1,

1.
Department of Mathematical Sciences, Ulsan National Institute of Science and Technology, Ulsan 689-798

Received: July 2014

Revised: April 2015

Published: May 2016

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Abstract

A spherical Radon transform whose integral domain is a sphere has many applications in partial differential equations as well as tomography. This paper is devoted to the spherical Radon transform which assigns to a given function its integrals over the set of spheres passing through the origin. We present a relation between this spherical Radon transform and the regular Radon transform, and we provide a new inversion formula for the spherical Radon transform using this relation. Numerical simulations were performed to demonstrate the suggested algorithm in dimension 2.

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Mathematics Subject Classification: Primary: 44A12, 65R10; Secondary: 92C55.

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