Tsybulska E. The development and mathematics modeling of three-dimension tomographic reconstruction methods

This thesis holds research in the area of mathematics modeling of tomography 3D-reconstruction, research of construction methods of reconstruction algorithms, developing and modeling of 3D-reconstruction algorithms. In according of the aims, there are developed new methods of tomography reconstruction to research objects which size is greater than CT-scaner detector system, there are offered methods to increase the reconstruction quality and speed. The analyse of complexity of developed algorithms and the comparison it with some known algorithms is done in the thesis. There are researched the methods of computing of line convolution which including into reconstruction algorithms, there are offered methods to reduction of comvolution complexity. The developed algorithm for computing of 1D convolution with 4D hypercomplex numbers is represented, the hypercomplex numerical system, which allows the reduction of convolution complexity, is determined. All described researches give the possibility to develop the program complex for modeling of tomography 3D-reconstruction and to show the results of reconstruction of mathematics phantoms structure.