Computing continuous models from discrete image data

A derivation of the optimal function for interpolating between CT (computed tomography) slices is presented. The data are assumed to be averaged over a slice thickness and overlapped. No assumptions about bandlimited data are made. Using DFT (discrete Fourier transform) techniques for the multiplication and inversion of circulant matrices, an interpolation function is easily computed which can be tailored to specific geometries and to the specific signal to noise ratios. For the case of 5-mm-thick slices taken at 3-mm intervals, the optimal resampling for low-noise measurements is almost-linear interpolation. As measurement noise increases, more low-pass filtering is included in the interpolation filter. The results predict that in cases of high signal-to-noise ratio, more complex interpolation functions would not improve the performance of those applications.<>