Once the principles of the logarithmic intensity plots are well understood, we can continue by presenting our proposed generalization to the 3D case.

The basic underlying assumption is that any (noisy) scanned PET image can be well approximated by an unknown higher resolution image convolved with a Gaussian kernel of unknown size. The sizes of the kernel for the in-plane and axial directions are assumed to be different, and they are estimated as the unknown coefficients in a multiple linear regression problem where the dependent variable is given by the logarithm of the image power spectrum.

The figure shows some examples of log-intensity plots from simulated non-isotropic Gaussian data, as well as from a human brain amyloid PET image. For all cases, the x-axis corresponds to the square distance to the origin in the frequency domain, while the y-axis is given by the logarithm of the image power spectrum in the Fourier space.

Notice that the resolution must be estimated from the leftmost side in the plots, which corresponds to small frequency values characterized by low values in the square distance to the origin.