On the determination of a function from cylindrical Radon transforms

Abstract

This paper is devoted to a Radon-type transform arising in Photoacoustic Tomography that uses integrating line detectors. We consider two situations: when the line detectors are tangent to the boundary of a cylindrical domain and when the line detectors are located on a plane. We present the analogue of the Fourier slice theorems for each case of the Radon-type transforms. Also, we provide several new inversion formulas, a support theorem, and stability estimate and necessary range condition results.