A PET reconstruction formulation that enforces non-negativity in projection space for bias reduction in Y-90 imaging

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. This paper investigates 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. Unlike the previously reported NEG-ML approach that modifies the Poisson log-likelihood to allow negative values, the new formulation retains the classical Poisson statistical model. 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 the methods 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 and NEG-ML and a regularized version thereof. Both our new method and NEG-ML allow more accurate quantification in all volumes of interest while yielding lower noise than the standard method. The performance of NEG-ML can degrade when its user-defined parameter is tuned poorly, while the proposed algorithm is robust to any count level without requiring parameter tuning.