PET Image Representation and Reconstruction based on Graph Filter

Due to count limitations, PET image reconstruction from low count data is challenging, resulting in the reconstructed image with high noise and blurred outline structures. By analyzing the graph spectrum of PET images reconstructed by different methods, we find that the most graph spectra of a high quality PET image generally reside in the low to middle frequencies in graph spectral domain. We therefore propose a novel PET image representation model based on a lowpass graph filter to represent PET images. Incorporating this model with MLEM, we propose a graph filter-based EM (GFEM) method to reconstruct the PET images with their graph spectra restricted to the low to middle frequencies. Extensive tests and comparisons show that GFEM achieves better visibility of small legions, and lower MSE, bias, and variance for dynamic PET image reconstruction than other methods, including MLEM with post-filter, the conventional regularization-based method, and kernelized EM (KEM). In the regions of interest, GFEM also achieves a better contrast recovery coefficient versus background noise standard deviation curve. Moreover, the graph filter-based representation model has a stronger representation ability than that of the kernel-based representation model in KEM, particularly in low count regions.