ABSTRACT
The concept of the computed tomography or computed X-ray tomography shows the process of projection data collection. On both sides of the analyzed object or image, which is assumed to be immovable, the X-ray set and detectors are disposed and revolved around the object by a small angle in certain time intervals. And the measurement data of radiation and detection of X-rays are collected along other directions. This chapter provides the solutions of the problem of reconstruction of the discrete image on the Cartesian lattice from projections of the image, which are based on the concepts of the tensor and paired transformations. It shows that a way of using the ray-sums, or line-integrals of the image, or real projection data, for exact reconstructing the discrete image. The chapter suggests that image reconstruction differs from the well-known methods of backprojection, iterative reconstruction, Fourier filtering, Radon filtering, and convolution filtering.
