The noise power spectrum of CT images

Abstract

An expression for the noise power spectrum of images reconstructed by the discrete filtered backprojection algorithm has been derived. The formulation explicitly includes sampling within the projections, angular sampling, and the two-dimensional sampling implicit in the discrete representation of the image. The effects of interpolation are also considered. Noise power spectra predicted by this analysis differ from those predicted using continuous theory in two respects: they are rotationally asymmetric, and they do not approach zero at zero frequency. Both of these properties can be attributed to two-dimensional aliasing due to pixel sampling. The predictions were confirmed by measurement of noise power spectra of both simulated images and images from a commercial x-ray transmission CT scanner.

Practical considerations for noise power spectra estimation for clinical CT scanners

“…2(b)). As can be seen, the 1D NPS increases linearly in the low spatial frequency range (due to the ramp filter) followed by the high‐frequency roll‐off (due to the low‐pass smoothing filter), resembling that reported by other published works for CT 4 , 20 , 21 , 30 …”

“…First, the 1D NPS was calculated from this reference image using a 128‐pixel ROI located in the image center and the image subtraction background removal method, with no window function applied, and was used as a reference ground truth NPS profile. The 128‐pixel ROI and the image subtraction background removal method used to compute this reference 1D NPS are the most commonly used calculation parameters as reported in other previous literature 4 , 20 , 21 , 30 . Five 2D NPS with radial symmetry, one for each ROI size used in this study (128, 96, 64, 48, 32), were generated from the reference 1D NPS profile using interpolation.…”

Biplane interventional pediatric system with cone‐beam CT: dose and image quality characterization for the default protocols

“…This shift is consistent with the image reconstruction filters that the manufacturer applies to the 5sDRc (smooth) and 5sDR‐L (standard) modes. The nonzero value of the 5sDR‐L NPS (and MTF) at the cutoff frequency indicates the presence of aliasing (29) . Finally, the low frequency peaks present in the teo NPS shown are due to structural noise.…”

A phantom study investigating the relationship between ground‐glass opacity visibility and physical detectability index in low‐dose chest computed tomography

“…This matched filter SNR (${\text{SNR}}_{\mathrm{M}}$) can be calculated by $SN{R}_M{\hspace{0.17em}}^2=2\pi true{\int }_0^{\infty }u\frac{S^{2}false(ufalse)MT{F}^{2}false(ufalse)}{NPSfalse(ufalse)}du$ where u is the spatial frequency and $Sfalse(ufalse)$ denotes the spatial frequency spectrum of the signal. The $\text{italicMTF}false(ufalse)$ and $\text{italicNPS}false(ufalse)$ were measured using a wire phantom and a water phantom, respectively, 13 , 24 , 25 , 26 , 27 as described in Material & Methods section C.2 and C.3 below. $Sfalse(ufalse)$ was calculated using a numerical simulation, as presented in section C.4 below.…”

“…The NPS for the water phantom image was calculated using a 2D Fourier transform according to a previously published method 13 , 26 , 27 . To generate a 1D NPS representation, radial rebinning of the data points comprising the 2D NPS into 25 frequency bins, was performed, and these bins were then averaged.…”