Isometry property and inversion of a spherical mean Radon transform with centers on a hyperplane

Abstract

The spherical mean Radon transform maps a suitable function f to the integral of f over a sphere. This transform is used in photoacoustic tomography based on the wave equation. There have been studies on the spherical mean Radon transform, including a method that uses an isometry property. In this paper, we demonstrate that the spherical mean Radon transform can be expressed as a convolution with specific (generalized) functions. Additionally, we provide an inversion formula for the spherical mean Radon transform, which is derived from the isometry property of the spherical mean Radon transform.