A Fixed-Point Iterative Method for Discrete Tomography Reconstruction Based on Intelligent Optimization

Discrete Tomography (DT) is a technology that uses image projection to reconstruct images. Its reconstruction problem, especially the binary image (0-1 matrix) has attracted strong attention. In this study, a fixed point iterative method of integer programming based on intelligent optimization is proposed to optimize the reconstructed model. The solution process can be divided into two procedures. First, the DT problem is reformulated into a polyhedron judgment problem based on lattice basis reduction. Second, the fixed-point iterative method of Dang and Ye is used to judge whether an integer point exists in the polyhedron of the previous program. All the programs involved in this study are written in MATLAB. The final experimental data show that this method is obviously better than the branch and bound method in terms of computational efficiency, especially in the case of high dimension. The branch and bound method requires more branch operations and takes a long time. It also needs to store a large number of leaf node boundaries and the corresponding consumption matrix, which occupies a large memory space.