Comprehensive Analysis of Alpha-Parametric Set for the Calculation of Intersection Lengths of Radiological Ray Path in Siddon's Algorithm Used in 3D Image Reconstruction

Abstract

The Siddon algorithm is one of the radiological ray path calculation tools used in 3D image reconstruction in medical imaging. In the algorithm, a set of alpha-parametric values is computed containing the length and index values where the voxel array of the x-ray intersects the x-y-z axes. In the alpha-set creation section of the Siddon algorithm, the set elements are sorted from small to large, but some elements have been noticed to have the same value in simulations. These elements are used to calculate which voxels are hit by the ray along the radiological path and at what ratio, but it was recognized that some values of the set were zero, which means some rays did not intersect some voxels at all. This situation may lead to data loss in 3D image reconstructions in medical imaging such as digital breast tomosynthesis (DBT) and computed tomography (CT) especially for huge dimensions such as size up to 800×800×50. Considering the mentioned problems, in this study, the effect of using or eliminating the same repetitive values in the alpha parametric set of the Siddon algorithm on calculations was investigated. To prove our proposal, we performed lossy and lossless 3D image reconstruction (100×100×50) of a synthetic phantom. Using special functions that do not take into account the duplicate values and exclude them in the algorithm solved the stated problems (lossless reconstruction). In this way, data loss that may occur in 3D image reconstruction was reduced since voxel indices and intersection lengths were matched correctly.