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

Abstract

Photoacoustic tomography is the mostwell-known example of a hybrid imaging method. In this article, we define a Radon-type transform arising in a version of photoacoustic tomography that uses integrating circular detectors and describe how the Radon transform integrating over all circles with a fixed radius is determined from this Radon-type transform.We consider three situations in which the centers of the circular detectors are located on a cylinder, on a plane, and on a sphere. This transform is similar to a toroidal Radon transform, which maps a given function to its integrals over a set of tori. We also study this object.