Tomographic task solution using a dichotomous discretization scheme in polar coordinates and partial system matrices invariant to rotations

Abstract

Objectives. The purpose of this work was to create an effective iterative algorithm for the tomographic reconstruction of objects with large volumes of initial data. Unlike the convolutional projection algorithm, widely used in commercial industrial and medical tomographic devices, algebraic iterative reconstruction methods use significant amounts of memory and typically involve long reconstruction times. At the same time, iterative methods enable a wider range of diagnostic tasks to be resolved where greater accuracy of reconstruction is required, as well as in cases where a limited amount of data is used for sparse-view angle shooting or shooting with a limited angular range.Methods. A feature of the algorithm thus created is the use of a polar coordinate system in which the projection system matrices are invariant with respect to the rotation of the object. This enables a signification reduction of the amount of memory required for system matrices storage and the use of graphics processors for reconstruction. Unlike the simple polar coordinate system used earlier, we used a coordinate system with a dichotomous division of the reconstruction field enabling us to ensure invariance to rotations and at the same time a fairly uniform distribution of spatial resolution over the reconstruction field.Results. A reconstruction algorithm was developed on the basis of the use of partial system matrices corresponding to the dichotomous division of the image field into partial annular reconstruction regions. A 2D and 3D digital phantom was used to show the features of the proposed reconstruction algorithm and its applicability to solving tomographic problems.Conclusions. The proposed algorithm allows algebraic image reconstruction to be implemented using standard libraries for working with sparse matrices based on desktop computers with graphics processors.

Keywords

• nondestructive technics
• x-ray computed tomography
• iterative algorithm
• system matrix