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A hybrid between region-based and voxel-based methods for Partial Volume correction in PET

Due to the limited resolution of Positron Emission Tomography (PET), loss of signal through Partial Volume is significant for small structures. Consequently, Partial Volume Correction (PVC) is often used in PET imaging to recover this lost signal within images. Numerous methods have been proposed, and can be divided in multiple ways. One division is the separation of methods utilising image based segmentation and those that perform image based deconvolution to recover resolution. We propose a new method for PVC, PARtially-Segmented Lucy-Richardson (PARSLR), that combines the image based deconvolution approach of the Lucy-Richardson (LR) Iterative Deconvolution Algorithm with a partial segmentation of homogenous regions. Such an approach is of value where reliable segmentation is possible for part but not all of the image volume or sub-volume. We evaluated the performance of PARSLR with respect to a region-based method (Rousset's method) and a deconvolution voxel-based method (LR) for partial volume correction by comparing how each method behaves in an environment of complete and accurate segmentation, and partial segmentation, on a 3D simulated medial temporal brain area including the hippocampus, as well as on a 2D physical brain phantom. Under complete and accurate segmentation, PARSLR showed agreement in recovery with the other methods. In an environment of partial segmentation, PARSLR recovered the hippocampus intensity with the most accuracy, with Rousset's method showing errors when too many regions were defined. With only one homogeneous background identified, errors were also observed when using Rousset, with the recovered value being smaller than the measured uncorrected data in these particular evaluations. In the 2D measured data for the brain phantom, PARSLR recovered with an error of −0.91%, with LR recovering to −5.23%, for a selected region of cortex. Rousset with a homogeneous background recovered with an error of −6.50%. With the remaining pixels set as individual regions, Rousset's method became ill-conditioned with an error of −157.00%. The method therefore showed good recovery in regions that are only partly segmentable. We propose that the approach is of particular importance for: studies with pathological abnormalities where complete and accurate segmentation across or with a sub-volume of the image volume is challenging; and regions of the brain containing heterogeneous structures which can not be accurately segmented from co-registered images.