An analytical inversion formula for the n-dimensional cylindrical Radon transform

Abstract We study the overdetermined problem of inverting the \(n\)-dimensional cylindrical Radon transform, which maps a function to its integrals over cylindrical surfaces. In practice, the cylindrical Radon transform arises in photoacoustic tomography as a measurement model for integrating line detectors. By exploiting its relationship with the Funk and Radon transforms, we derive an analytic inversion formula for the cylindrical Radon transform. We also present numerical implementations of the proposed inversion algorithm, demonstrating its numerical robustness under discretization effects and moderate noise.