Quantifying the Partial Volume Effect in PET Using Benford's Law

Partial volume (PV) correction techniques in PET or SPECT represents a key step in image quantification methods. The PV effect arises because of the blurring induced by the imaging system's point spread function (PSF), producing intra-voxel mixing of the signals arising from different functional tissue classes. Quantification of this effect is often required to recover the mixing components within a group of voxels, from whence the true tissue concentration in a given volume or region can be estimated. In this work we consider a probabilistic methodology that uses a phenomenological distribution known as Benford's law to quantify the partial volume effect. We establish for the first time, that the probability distribution of voxels subjected to the PV effect in discrete volumetric data can be well described by Benford's law. The probabilistic framework devised here can be applied generically across different imaging modalities including PET and SPECT. Results from simulated data are presented, along with a PET phantom study utilizing registered processed CT data as ground truth, to determine the quality of the resulting probabilistic voxel classification scheme. For a water filled hot insert using a 5:1 insert:background activity concentration, we find an overall voxel RMS error of 3% (compared to ground truth) in the estimated voxel mixing vectors. This error rises to 8% for a cold air-filled insert in a warm background.