Deconvolution-based partial volume correction of PET images with parallel level set regularization

The partial volume effect (PVE), caused by the limited spatial resolution of positron emission tomography (PET), degrades images both qualitatively and quantitatively. Anatomical information provided by magnetic resonance (MR) images has the potential to play an important role in partial volume correction (PVC) methods. Post-reconstruction MR-guided PVC methods typically use segmented MR tissue maps, and further, assume that PET activity distribution is uniform in each region, imposing considerable constraints through anatomical guidance. In this work, we present a post-reconstruction PVC method based on deconvolution with parallel level set (PLS) regularization. We frame the problem as an iterative deconvolution task with PLS regularization that incorporates anatomical information without requiring MR segmentation or assuming uniformity of PET distributions within regions. An efficient algorithm for non-smooth optimization of the objective function (invoking split Bregman framework) is developed so that the proposed method can be feasibly applied to 3D images and produces sharper images compared to PLS method with smooth optimization. The proposed method was evaluated together with several other PVC methods using both realistic simulation experiments based on the BrainWeb phantom as well as in vivo human data. Our proposed method showed enhanced quantitative performance when realistic MR guidance was provided. Further, the proposed method is able to reduce image noise while preserving structure details on in vivo human data, and shows the potential to better differentiate amyloid positive and amyloid negative scans. Overall, our results demonstrate promise to provide superior performance in clinical imaging scenarios.