# About one method of parallelization of calculations during the reconstruction of a tomographic image

## TL;DR

This paper introduces a novel parallelization method for tomographic image reconstruction that leverages matrix symmetry and voxel numbering to split the problem into smaller, independent systems, enabling faster computations.

## Contribution

The proposed method uniquely exploits matrix symmetry and voxel numbering to divide the system into smaller, independent systems for parallel processing in image reconstruction.

## Key findings

- Matrices of the divided systems are four times smaller
- The method reduces matrix dispersion
- Enables parallel computation of tomographic reconstructions

## Abstract

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.