Algorithm for Reconstruction of Three-Dimensional Images in X-Ray Computed Tomography with a Cone Beam of Radiation

Purpose: Development of an algorithm for the reconstruction of three-dimensional images in X-ray computed tomography with a cone beam. Material and methods: A new approach to the development of the reconstruction algorithm is proposed. The algorithm is based on the exact analytical representation of the 3D Radon transform of the projection data. For such a representation, an iteration-invariant point spread function (PSF) is introduced. From the existing approximate algorithms of Feldkamp, Katsevich and other authors, the developed algorithm differs in increased accuracy, is applicable for high-performance spiral X-ray tomography, and provides a practical design of the X-ray optical path of the tomograph. Results: Mathematical modeling of the developed three-dimensional reconstruction algorithm for the helical trajectory of the radiation source was performed; satisfactory results were obtained on a phantom model simulating an object of study with contrast inserts. The influence of the distance of the radiation source from the center of coordinates with respect to the radius of the object of study is shown, for which a mathematical model of a special phantom in the form of a cube, consisting of separate uniform elliptical plates (ellipsoids) of the same density, was developed. The quality of the reconstructed tomographic images was assessed through by measurement of the difference between the image of the section of the phantom model and the reconstructed image, presented as the root mean square error. Conclusion: Studies have shown that for the ratio of the radius of the spiral trajectory to the radius of the object (R/Rm ), equal to about 3.0, i.e. at sufficiently large angles of the radiation cone of the source, the developed algorithm for three-dimensional reconstruction with a cone beam of radiation gives a tomographic image of high quality. This can be applied in the devel-opment of medical X-ray computed tomography.