Bias in iterative reconstruction of low-statistics PET data: Benefits of a resolution model

Ordered-subset expectation maximization (OSEM) is a widely used method of reconstructing PET data. Several authors have reported bias when reconstructing frames containing few counts via OSEM, although the level of bias reported varies substantially. Such bias may lead to errors in biological parameters as derived via dynamic PET. We examine low-statistics bias in OSEM reconstruction of patient data and estimate the subsequent errors in biological parameter estimates. Patient listmode data were acquired during a [
¹¹
C]-DASB scan using a brain PET scanner, the high resolution research tomograph (HRRT). These data were sub-sampled to create many independent, low-count replicates. Each replicate was reconstructed with and without the use of an image based resolution model (PSF), from which bias and variance were calculated as a function of the noise equivalent counts (NEC). Time-activity curves were subsequently generated by Monte Carlo simulation and used to study the propagation of bias from the images into the biological parameters of interest, for which noise and bias were based on the NEC. The investigation was complemented by simulation of a PET scanner. Significant bias was observed when reconstructing data of low statistical quality, for both human and simulated data. For human data, this bias was substantially reduced by including a PSF model (e.g. caudate head, 1.7 M NEC, -5.5% bias with PSF, -13% bias without PSF). For the observed levels of bias, Monte Carlo simulations predicted biases in the binding potential of -4 and -10% (with/without PSF). The use of the PSF changed the variance characteristics of the images, reducing variance at the voxel level for low to moderate numbers of iterations. We conclude that OSEM reconstruction of dynamic PET data can yield parameter estimates of acceptable accuracy (for DASB), despite producing biased images at low statistics. This is however dependent upon the application. The use of a resolution model is shown to reduce bias and is thus recommended. The most likely mechanism for this reduction is the suppression of noise. The magnitude of the bias for other tracers and methods of data analysis is yet to be evaluated.