Reducing Bias in Y-90 PET Images by Enforcing Non-Negativity in Projection Space

Most existing PET image reconstruction methods impose a nonnegativity constraint in the image domain that is natural physically, but can lead to biased reconstructions. This bias is particularly problematic for Y-90 PET because of the low probability positron production and high random coincidence fraction. We propose a new PET reconstruction formulation that enforces nonnegativity of the projections instead of the voxel values. This formulation allows some negative voxel values thereby potentially reducing bias. To relax the non-negativity constraint embedded in the standard methods for PET reconstruction, we used an Alternating Direction Method of Multipliers (ADMM). Because choice of ADMM parameters can greatly influence convergence rate, we applied an automatic parameter selection method to improve the convergence speed. We investigated several variants differentiated by the base model and the constraint condition using lung to liver slices of XCAT phantom. We simulated low true coincidence count-rates with high random fractions corresponding to the typical values from patient imaging in Y-90 microsphere radioembolization. We compared our new methods with standard reconstruction algorithms. As the proposed algorithm iterates, the new method reduces the bias in cold spot while yielding lower noise than the standard method. The new model improves the quantification in all regions of interest when the methods achieve similar level of noise in the liver. The improvements with the new method are especially notable when simulating conditions corresponding to patients with lower activity administration (i.e., higher random fractions).