Overview of the logarithmic intensity of plots of two-dimensional real images. A logarithm intensity plot is a scatter plot of the logarithm of the square norm of the image Fourier transform against the square distance from the origin in the frequency domain. The full-width half-maximum (FWHM) of the image is determined by a linear regression.
Given the current limitations involving the Hoffman phantom-based approach, we introduce a computational approach for harmonization of brain PET image spatial resolution without phantoms.
Our proposed approach is based on the generalization of the 2D logarithmic intensity plots in the Fourier domain to the 3D case. Such generalization does not only apply to the estimation of isotropic resolution in 3D, but also allows for the consideration of different in-plane and axial resolution spatial estimations.
Before continuing with the explanation of our new method, let’s observe the diagram and briefly describe the fundamentals of the logarithmic intensity plots for the estimation of the spatial resolution in real 2D images.
The basic element in the original 2D logarithmic intensity plots approach is to plot the logarithm of the square norm of the image Fourier transform against the square distance from the origin in the frequency domain. Once in this plot, the unknown width of the Gaussian kernel is determined by a linear regression using the smallest square frequency values only.