Paired Transform Slice Theorem of 2-D Image Reconstruction from Projections

This paper discusses the paired transform-based method of reconstruction of 2-D images from their projections. The complete set of basic functions of the 2-D discrete paired transform are defined by specific directions, i.e. the transform is directional and can be calculated from the projection data. A simple formula is presented for image reconstruction without calculating the 2-D discrete Fourier transform in the case, when the size of image is L^r × L^r, when L is prime. The image reconstruction is described by the discrete model that is used in the series expansion methods of image reconstruction. The proposed method of reconstruction has been implemented and successfully applied for modeled images on Cartesian grid of sizes up to 256×256.