  A new method for solving systems of linear algebraic equations of a special
type arising in solving problems of image reconstruction has been proposed.
This method, due to a certain symmetry of the matrix and the choice of the
voxel numeration method for two-dimensional problems, allows us to divide the
initial system of algebraic equations into two independent systems, which
enables us to carry out the calculation in parallel. The dimension of the
matrices of the resulting systems is 4 times less than the dimension of the
original matrix, and these matrices are less dispersed.
