The noise power spectrum in computed X-ray tomography

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Abstract
An expression was derived showing that the 2-dimensional noise power spectrum of computed X-ray tomography was proportional to G(k) 2/k where k was the radial spatial frequency, and G(k) was the 1-dimensional corrective filter used in the filtered back-projection reconstruction technique. Predicted noise power spectra apparently compared well with those estimated from CT [computed tomography] reconstructions of simulated noise for the ramp filter and Hanning-weighted ramp filter. A consequence of the nonuniform shape of the noise power spectrum was that statistical noise in CT reconstruction was correlated from point to point. Because of this correlation when the reconstructed CT values were averaged over some region, the uncertainty of the average depends on the shape and area of the region. This dependence was confirmed by computer simulations.

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