Відновлення розривних функцій двох змінних з використанням методу скінченних сум Фур’є, Фейєра та сплайнів

Abstract

This work is focused on the reconstruction of discontinuous functions of two variables based on their known projection data obtained from a CT scanner. Three solution methods are implemented and compared. When the Fourier or Fejér finite sum methods are used directly, the Gibbs phenomenon occurs. The method based on discontinuous splines allows to eliminate it when used in combination with the methods mentioned above. To demonstrate this, a computational experiment was conducted, and the results confirm the effectiveness of the method.