Partial volume correction of PET image data using geometric transfer matrices based on uniform B-splines

Objective. Most methods for partial volume correction (PVC) of positron emission tomography (PET) data employ anatomical segmentation of images into regions of interest. This approach is not optimal for exploratory functional imaging beyond regional hypotheses. Here, we describe a novel method for unbiased voxel-wise PVC.Approach.B-spline basis functions were combined with geometric transfer matrices to enable a method (bsGTM) that provides PVC or alternatively provides smoothing with minimal regional crosstalk. The efficacy of the proposed method was evaluated using Monte Carlo simulations, human PET data, and murine functional PET data.Main results.In simulations, bsGTM provided recovery of partial volume signal loss comparable to iterative deconvolution, while demonstrating superior resilience to noise. In a real murine PET dataset, bsGTM yielded much higher sensitivity for detecting amphetamine-induced reduction of [¹¹C]raclopride binding potential. In human PET data, bsGTM smoothing enabled increased signal-to-noise ratios with less degradation of binding potentials relative to Gaussian convolution or non-local means.Significance.bsGTM offers improved performance for PVC relative to iterative deconvolution, the current method of choice for voxel-wise PVC, especially in the common PET regime of low signal-to-noise ratio. The new method provides an anatomically unbiased way to compensate partial volume errors in cases where anatomical segmentation is unavailable or of questionable relevance or accuracy.