2.2.2. Noise power spectrum (NPS)

Texture properties of CT image noise were assessed by computing the NPS (i.e. the spatial frequency distribution of noise) [65, 66]:

where f_x/f_y are the spatial frequencies along the main orthogonal directions, Δx/Δy are the voxel sizes, N_x/N_y are the number of voxels for each direction, FFT is the two-dimensional (2D) fast Fourier transform, ROI_noise(x,y) is the local value of an "only-noise" ROI and < > indicates the ensemble average (i.e. the average across measurements performed on a number of ROIs). In particular, for each acquisition, an ensemble of 5 ROIs (64 pixels × 64 pixels) was selected from the acquisition slab central image of the uniform CTP486 phantom module. Given the radial symmetry of the 2D NPS, radial profiles along many directions were averaged in order to obtain the one dimensional NPS curve. In particular, the selection of radial profiles was carried out every 10° over 360°, obtaining a total of 36 radial profiles.

In order to estimate peak position, NPS curves were fitted by using a specific peak function (namely "InvsPoly") implemented in Origin:

where x_c is the peak position, A/A₁/A₂/A₃ are coefficients related to the amplitude of the peak, w is a parameter related to the width of the curve and y₀ is an offset.