Voxel-based partial volume correction of amyloid PET images incorporating non-local means regularization

Amyloid PET imaging is increasingly utilized to assess Alzheimer's disease. Nonetheless, PET imaging can be significantly degraded by the partial volume effect (PVE). This issue has been tackled via a number of post-reconstruction partial volume correction (PVC) methods. In our work, we proposed a voxel-based PVC method using non-local means (NLM) regularization under the weighted least squares framework that models the point-spread function of the PET system. The NLM algorithm has been proposed to suppress image noise while preserving edge information for natural images. This algorithm utilizes the high degree of information redundancy that typically exists in images and reduces image noise by replacing each pixel intensity with a weighted average of its non-local neighbors. Based on its advanced property, we propose to employ NLM as a regularization term in PET PVC. For a penalized weighted least squares (PWLS) objective function, we used the Gauss-Seidel (GS) optimization algorithm regularized with one-step-late (OSL) framework. Under the assumption of independent, identically-distributed (iid) Gaussian noise, the PWLS framework becomes standard least squares. When the steepest descent scheme is applied to the problem, it leads to the iterative 'reblurred' Van Citter (VC) method. We tried both the VC method, and GS which involves a more sophisticated step-size method. In any case, the iid assumption is especially violated in OSEM reconstruction where the variance image is roughly proportional to the image (thus not uniform as in FBP). In the present work, we assessed the impact of appropriate variance weighting, as well as added NLM regularization. Our results demonstrate that statistical weighting improved quantitative bias vs. noise performance; and also, NLM regularization method exhibits improved performance. These were especially the case in the small regions relevant in Alzheimer's disease research.