Properties of a parameterization of radon projection by the reconstruction on circular disk

An angular parameterization of parallel Radon projections referred to in this paper as ψ-parameterization is discussed in relevance to the efficiency of reconstruction from fan data. The fact that the ψ-parameterization coincides with the equiangular fan beam parameterization allows us to develop a simple and efficient approach useful for the reconstruction from fan data. Within this approach parallel projections are approximated by groups of semi-parallel rays. The reconstruction is carried out directly, i.e. without any modification of original data, at the speed which is comparable or even higher than that of the parallel Filtered Back Projection (FBP) algorithm.