The noise power spectrum in computed X-ray tomography.

An expression is derived showing that the two-dimensional noise power spectrum of computed X-ray tomography is proportional to [G(k)]2/k where k is the radial spatial frequency and G(k) is the one-dimensional corrective filter used in the filtered back-projection reconstuction technique. It is shown that predicted noise power spectra compare well with those estimated from CT reconstructions of simulated noise for both the ramp filter and the Hanning-weighted ramp filter. A consequence of the non-uniform shape of the noise power spectrum is that statistical noise in CT reconstructions is correlated from point to point. Because of this correlation when the reconstructed CT values are averaged over some region, the uncertainty of the average depends on the shape of the region as well as its area. This dependence is confirmed by computer simulations.