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

Sunghwan Moon | Zendy

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Inversion 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 andamp 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

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