A Radon-type transform arising in photoacoustic tomography with circular detectors: spherical geometry

In this paper, we propose a detector geometry for photoacoustic tomography that offers the practical advantage that it could be implemented with a single circular detector. The Radon-type transform that arises can be decomposed into the spherical Radon transform and the Funk–Minkowski transform. An inversion formula and a range description are obtained by combining existing inversion formulas and range descriptions for the spherical Radon transform and the Funk–Minkowski transform. Numerical simulations are performed to demonstrate our proposed algorithm.