Image Reconstruction from limited-angle range projections

This paper describes a new approach for reconstructing images from a finite number of projections. The ray-integrals of the image f (x, y) are transformed uniquely into the ray-sums of the discrete image f(n,m) on the Cartesian lattice. This transformation allows for calculating the tensor representation of the discrete image, when the image is considered as the sum of direction images, or splitting-signals carrying the spectral information of the image at frequency-points of different subsets that cover the Cartesian lattice. These subsets are intersected and this property of redundancy is used to reduce the angular range of projections. The proposed approach is presented for parallel projections and the continuous model. Preliminary results show very good results of image reconstruction when the angular range scanned is 27 degrees and down to 10 degrees.