Sampling in Fan Beam Tomography

Abstract

In fan beam tomography, functions in $\mathbb{R}^2 $ are constructed from integrals along straight lines emanating from a finite number of sources sitting on a circle around the reconstruction region. Using a sampling theorem for periodic functions and asymptotic estimates for the Fourier transform of the fan beam transform, the exact sampling conditions are found for standard fan beam scanning necessary to obtain a certain resolution. New efficient sampling schemes and corresponding reconstruction algorithms are also found. These sampling schemes need significantly less data to obtain a certain resolution than a standard fan beam geometry. The correctness of the sampling conditions for standard fan beam scanning and the superiority of the new schemes are shown by computer simulations.