PET image reconstruction and denoising on hexagonal lattices

Nuclear imaging modalities like Positron emission tomography (PET) are characterized by a low SNR value due to the underlying signal generation mechanism. Given the significant role images play in current-day diagnostics, obtaining noise-free PET images is of great interest. With its higher packing density and larger and symmetrical neighbourhood, the hexagonal lattice offers a natural robustness to degradation in signal. Based on this observation, we propose an alternate solution to denoising, namely by changing the sampling lattice. We use filtered back projection for reconstruction, followed by a sparse dictionary based denoising and compare noise-free reconstruction on the Square and Hexagonal lattices. Experiments with PET phantoms (NEMA, Hoffman) and the Shepp-Logan phantom show that the improvement in denoising, post reconstruction, is not only at the qualitative but also quantitative level. The improvement in PSNR in the hexagonal lattice is on an average between 2 to 10 dB. These results establish the potential of the hexagonal lattice for reconstruction from noisy data, in general.