It is well known that the projection measurements of a uniform cylinder result in a higher density of detected x-ray quanta near the edge of the cylinder than near its center in the absence of a compensation wedge or water bolus. If the noise in the projection measurements is dominated by the statistical fluctuations in the number of detected quanta, the rms projection noise is largest near the center of the cylinder and drops near the edge. The rms noise in the CT reconstruction will then be largest in the center of the reconstructed circle and smallest near the perimeter. The noise in such a reconstruction is decidedly non-stationary.
It is feasible to perform a noise power spectral analysis of the above image even though the noise is not stationary. The symmetry in the projection measurement geometry implies that the noise at a constant radius from the center of the circle will be of uniform character. Further, at a fixed radius the spatial correlations in the noise resulting from the CT reconstruction algorithm will be constant provided they are expressed in terms of a tangential-radial coordinate system. The noise power spectrum (NPS) may be estimated by using subsamples of the image confined to an annulus centered on the circle. The 2-D NPS from these subsamples are averaged (to reduce the statistical fluctuations in the estimate of the power spectrum) only after they are rotated to align their tangential and radial frequency axes. Thus, statistically significant NPS for a given average radius may be estimated from a single image.
This technique is demonstrated for Delta 2020 water phantom scans. Since this CT scanner does not yet employ a compensation wedge [bow-tie filter], a large reduction in the NPS along the radial frequency axis is observed. The dependence of the NPS upon the average radius is consistent with a calculation of the density of detected x-ray quanta together with a small component of background noise. This effect is much smaller for scanners with compensation wedges (EMI 5005 and GE 8800).
Another interesting phenomenon is demonstrated for a GE 8800, which is a third-generation scanner with a rotating fan-beam geometry. The standard 2-D NPS for a half-scan (180 deg + fan angle) from this scanner shows a narrow dip along a radial line through the origin, presumably because of the averaging of redundant projection rays in a specific direction.
Keywords: CT reconstruction noise, two-dimensional noise power spectrum (NPS), nonstationary noise, radial and tangential components, x-ray quanta, noise-equivalent quanta (NEQ), bow-tie filter
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