Open AccessInversion of the spherical Radon transform on spheres through the origin using the regular Radon transform
Author(s) -
Sunghwan Moon
Publication year - 2016
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2016.15.1029
Subject(s) - radon transform , radon , spheres , spherical mean , inversion (geology) , mathematical analysis , integral transform , spherical harmonics , mathematics , physics , geometry , geology , quantum mechanics , paleontology , astronomy , structural basin
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.clos