Noise Power Spectrum calculation I want to compute the 1-D noise power spectrum (NPS) for a uniform CT image. The equation of the 2D NPS is as following:
$$
NPS(f_x, f_y) =\frac{1}{N}\sum_{i=1}^N|DFT_{2D}[I_i(x,y)-\bar{I}_i]^2\frac{\Delta_x\Delta_y}{N_xN_y}
$$
whre $DFT$ is the discrete fourier transform, $I_i$ is a ROI, $\bar{I}$ is the mean of the ROI. The 1-D dimensional (or radial) NPS is defined as:
$$
f_r = \sqrt{f_x^2+f_y^2}
$$
Assuming only one ROI and obviating the units factor, I compute the 2D NPS as:
fft = np.fft.fft2(roi-np.mean(roi))
fft = np.fft.fftshift(fft)    
NPS_2D = np.abs(fft)**2

How can I compute from here the 1-D radial NPS?
Obtain parallel beam sinogram of your image, then take the FFT of the sinogram (if you consider the Fourier transform in polar coordinate, then Fourier slice theorem tell us value of Fourier transform over a radial line at a given angle is equal to the fourier transform of the projection over that angle), after that average the power over different angles. To obtain sinogram, if there isn't any available function, you could rotate the image by desired angle, then sum over columns or rows.