Mapping between Digital and Continuous Projections via the Discrete Radon Transform in Fourier Space

This paper seeks to extend the Fourier space properties of the discrete Radon transform, R(t,m), proposed by Matus and Flusser in [1], to expanded discrete projections, R(k, θ), where the wrapping of rays is removed. This expanded mode yields projections more akin to the continuous space sinogram. It is similar to the Mojette transform defined in [2], but has a pre-determined set of discrete projection angles derived from the Farey series [3]. It is demonstrated that a close approximation to the sinogram of an image can be obtained from R(k, θ), both in Radon and Fourier space. This investigation is undertaken to explore the possibilities of applying this mapping to the inverse problem, that of obtaining discrete projection data from continuous projection data as a means of efficient tomographic reconstruction that requires minimal interpolation and filtering.