Method of G-particles for image reconstruction from a finite number of projections

To reconstruct the image from a finite number of projections, the concept of the point map of projections is described. Each projection is described by the corresponding set of line-integrals along a finite set of rays. The image element with its geometry is considered as a particle, or G-particle which is described by the field function. The map of each particle is considered in the form of a matrix which describes all rays passing through this particle. The concept of the field functions of particles is described as a number of rays passing through the particles with others at the same time. The consideration of the field functions for these G-particles leads to a representation of the image by the field functions, and this representation allows for reconstructing the image from its projections. The reconstruction f(n,m) of the image f(x, y) on the 64x64 and 128x128 Cartesian lattices by the method of G-particles is demonstrated on the images with random rectangles.