An Investigation of Computerized Tomography by Direct Fourier Inversion and Optimum Interpolation

In this paper an exact interpolation formula forms the basis for reconstructing computerized tomographic (CT) imagery by direct Fourier methods. Practical variations of exact interpolation are compared with other interpolation methods (i.e., nearest neighbor, etc.) and are shown to yield superior imagery. Images produced by the direct Fourier approach using near-exact interpolation are shown to be equal in quality with those produced by filtered convolution backprojection (FCBP). Moreover, the direct Fourier approach computes an image in O(N2 log N) time versus O(N3) for the FCBP method.