Direct Fourier transform techniques in 3 D image reconstruction

Several algorithms for the reconstruction of an unknown spatially limited function from M of its projections are considered. These algorithms all perform the reconstruction in Fourier space by exploiting the projection theorem. All of these algorithms first sample the projections, then use these samples to compute their Fourier transforms. An interpolation is then performed in Fourier space, followed by an inverse two-dimensional Fourier transform. Special attention is paid to the sampling errors introduced and to the errors introduced by various interpolation methods. Several published interpolation methods are compared. The direct Fourier algorithms are also compared to the widely-used convolution method. Application to multidimensional tomographic projections is indicated.