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

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

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