Fast Inversion of the Exponential Radon Transform by Using Fast Laplace Transforms

Abstract. The Fourier slice theorem used for the standard Radon transform generalizes to a Laplace counterpart when considering the exponential Radon transform. We show how to use this fact in combination with using algorithms for unequally spaced fast Laplace transforms to construct fast and accurate methods for computing, both the forward exponential Radon transform and the corresponding back-projection operator. Moreover, we show how to use this result for inverting data modeled by the exponential Radon transform, both in the case of complete and incomplete data measurements. For the case of incomplete data, we show how to formulate the reconstruction problem as a deconvolution problem that only uses standard FFT after some initial computations using Laplace transforms.