МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ТОМОГРАФІЧНОЇ РЕКОНСТРУКЦІЇ З ВИКОРИСТАННЯМ АЛГЕБРАЇЧНИХ МЕТОДІВ

The work is dedicated to the development of algorithms for reconstructing functions from known projection data received from a computer tomograph. Algebraic methods were used for function reconstruction. The methods are based on the Radon transform and are reduced to solving a system of algebraic equations, which is overdetermined. Regularization methods and iterative methods were used to solve it. Piecewise-linear functions were chosen as coordinate functions, as well as functions built on the basis of interpolation operators. Numerical implementation of the methods was carried out. Test problems were considered. Satisfactory results were obtained.