The paper describes the implementation and use of recently developed DFT and DCT based discrete sinc-interpolation algorithms for the direct Fourier method of reconstructing images from projections. DFT based discrete sinc-interpolation is the only completely reversible discrete interpolation technique. DCT based discrete sinc-interpolation algorithm implements the same interpolation kernel that of the DFT based method and allows to avoid its boundary affect artifacts. It is also computationally more efficient. Two modifications of the DCT based interpolation for tomographic reconstruction are suggested: interpolation by global zooming of 1-D DFT spectra of projections and interpolation with variable zooming factor along the angle coordinate. The latter allows to substantially reduce the computational complexity without compromising interpolation accuracy. Results of comparative numerical simulation of suggested algorithms show a good image reconstruction quality with a reduced level of artifacts.