Reconstruction of the image on the Cartesian lattice from a finite number of projections in computed-tomographic imaging

The reconstruction of the image f(x, y) is from a finite number of projections on the discrete Cartesian lattice N x N is described. The reconstruction is exact in the framework of the model, when image is considered as the set of N-2 cells, or image elements with constant intensity each. Such reconstruction is achieved because of the following two facts. Each basis function of the tensor transformation is determined by the set of parallel rays, and, therefore, the components of the tensor transform can be calculated by ray-sums. These sums can be determined from the ray-integrals, and we introduce here the concept of geometrical, or G-rays to solve this problem. The examples of image reconstruction by the proposed method are given, and the reconstruction on the Cartesian lattice 7 x 7 is described in detail.