Evaluation of Imaging Systems Using the Posterior Variance of Emission Counts

Abstract

We investigate an approach to evaluation of emission-tomography (ET) imaging systems used for region-of-interest (ROI) estimation tasks. In the evaluation we employ the concept of "emission counts" (EC), which are the number of events per voxel emitted during a scan. We use the reduction in posterior variance of ROI EC, compared to the prior ROI EC variance, as the metric of primary interest, which we call the "posterior variance reduction index" (PVRI). Systems that achieve a higher PVRI are considered superior to systems with lower PVRI. The approach is independent of the reconstruction method and is applicable to all photon-limited data types including list-mode data. We analyzed this approach using a model of 2-D tomography, and compared our results to the classical theory of tomographic sampling. We found that performance evaluations using the PVRI index were consistent with the classical theory. System evaluation based on EC posterior variance is an intuitively appealing and physically meaningful method that is useful for evaluation of system performance in ROI quantitation tasks.

Capability of MLEM and OE to Detect Range Shifts With a Compton Camera in Particle Therapy

“…The noninformative flat prior distribution on which the current OE implementation relies could be substituted by more informative priors which can compensate for the little information provided by the measured data. Additionally, other capabilities of OE could be exploited, e.g., to estimate the confidence interval of the solution, or optimize the imaging system [40]. Further improvements in the performance of both algorithms might be achieved by optimizing FOV and voxel size.…”

Time-of-flight PET image reconstruction using origin ensembles

“…For the purpose of MMSE-OE reconstruction, we propose the following two modifications to the original OE updating scheme of Sitek (2008, 2011, 2012) and Sitek and Moore (2013): (1) sequential updating of all event locations (so-called single-site updating ) may be used. Such linear iteration over the events allows for a very fast data access, and is of minor impact on the behavior of the Markov chain (18) since all events can be treated as statistically and geometrically almost independent of one another (see Leahy and Qi (2000)).…”

“…We demonstrate our approach using LORs again, and note that a generalization to VORs is possible. As proposed by Sitek (2008, 2011, 2012) and Sitek and Moore (2013), it is sufficient to initially assign each event k = 1, …, K to an arbitrary volume element i with a ij k > 0. However, this can result in a weak starting state of the OE Markov chain.…”

“…Alongside other applications of the OE algorithm (see Sitek (2012) and Sitek and Moore (2013), for example), this method can be used to estimate the emission density λ in the following, conceptually straightforward manner. First, the MMSE estimate for each emission count n i is computed.…”

“…We have previously described an alternative to FP/BP-driven algorithms that reconstructs the image entirely in the image domain, i.e. without the use of FP and BP operations: origin ensemble (OE) reconstruction (Sitek 2008, Sitek 2011, Sitek 2012, Sitek and Moore 2013). Its convergence to steady state and to a solution very close to that of EM was demonstrated in (Sitek 2008, Sitek 2011, Sitek 2012).…”