Bootstrap methods for estimating PET image noise: experimental validation and an application to evaluation of image reconstruction algorithms

A tomographic spatial-unfolding method for Compton gamma imaging measurements

An advanced spatial-unfolding technique capable of reconstructing the activity distribution within an exclusion zone from Compton gamma imager measurements taken outside of it is introduced. Although the method is generally applicable to extended sources, we demonstrate it here on a calibrated Cs-137 point source through Monte Carlo simulation studies as well as with measurements made using a Silicon Compton Telescope for Safety and Security (SCoTSS) gamma imager. For synthetic data the method accurately reconstructs the total activity contained within the mapped zone of interest, even when the size of the basis elements used to reconstruct the activity distribution is larger than the source itself. For experimental data, the method reliably located the source but underestimated its activity by up to 17%. This is accurate enough for real-world security applications. The underestimation is likely due to effects not yet included in the simulated response of the detector. The method has widespread applicability in the radiological/nuclear safety and security field, particularly for scenarios in which a threat material or contaminated area lies within a no-entry or no-fly zone.

A Generalized Linear modeling approach to bootstrapping multi-frame PET image data

PET imaging is an important diagnostic tool for management of patients with cancer and other diseases. Medical decisions based on quantitative PET information could potentially benefit from the availability of tools for evaluation of associated uncertainties. Raw PET data can be viewed as a sample from an inhomogeneous Poisson process so there is the possibility to directly apply bootstrapping to raw projection-domain list-mode data. Unfortunately this is computationally impractical, particularly if data reconstruction is iterative or the acquisition protocol is dynamic. We develop a flexible statistical linear model analysis to be used with multi-frame PET image data to create valid bootstrap samples. The technique is illustrated using data from dynamic PET studies with fluoro-deoxyglucose (FDG) and fluoro-thymidine (FLT) in brain and breast cancer patients. As is often the case with dynamic PET studies, data have been archived without raw list-mode information. Using the bootstrapping technique maps of kinetic parameters and associated uncertainties are obtained. The quantitative performance of the approach is assessed by simulation. The proposed image-domain bootstrap is found to substantially match the projection-domain alternative. Analysis of results points to a close relation between relative uncertainty in voxel-level kinetic parameters and local reconstruction error. This is consistent with statistical theory.

Spatial Auto-Regressive Analysis of Correlation in 3-D PET With Application to Model-Based Simulation of Data

When a scanner is installed and begins to be used operationally, its actual performance may deviate somewhat from the predictions made at the design stage. Thus it is recommended that routine quality assurance (QA) measurements be used to provide an operational understanding of scanning properties. While QA data are primarily used to evaluate sensitivity and bias patterns, there is a possibility to also make use of such data sets for a more refined understanding of the 3-D scanning properties. Building on some recent work on analysis of the distributional characteristics of iteratively reconstructed PET data, we construct an auto-regression model for analysis of the 3-D spatial auto-covariance structure of iteratively reconstructed data, after normalization. Appropriate likelihood-based statistical techniques for estimation of the auto-regression model coefficients are described. The fitted model leads to a simple process for approximate simulation of scanner performance-one that is readily implemented in an R script. The analysis provides a practical mechanism for evaluating the operational error characteristics of iteratively reconstructed PET images. Simulation studies are used for validation. The approach is illustrated on QA data from an operational clinical scanner and numerical phantom data. We also demonstrate the potential for use of these techniques, as a form of model-based bootstrapping, to provide assessments of measurement uncertainties in variables derived from clinical FDG-PET scans. This is illustrated using data from a clinical scan in a lung cancer patient, after a 3-minute acquisition has been re-binned into three consecutive 1-minute time-frames. An uncertainty measure for the tumor SUV_max value is obtained. The methodology is seen to be practical and could be a useful support for quantitative decision making based on PET data.

The Gamma Characteristic of Reconstructed PET Images: Implications for ROI Analysis

The basic emission process associated with positron emission tomography (PET) imaging is Poisson in nature. Reconstructed images inherit some aspects of this-regional variability is typically proportional to the regional mean. Iterative reconstruction using expectation-maximization (EM), widely used in clinical imaging now, imposes positivity constraints that impact noise properties. This paper is motivated by the analysis of data from a physical phantom study of a PET/CT scanner in routine clinical use. Both traditional filtered back-projection (FBP) and EM reconstructions of the images are considered. FBP images are quite Gaussian, but the EM reconstructions exhibit Gamma-like skewness. The Gamma structure has implications for how reconstructed PET images might be processed statistically. Post-reconstruction inference-model fitting and diagnostics for regions of interest are of particular interest. Although the relevant Gamma parameterization is not within the framework of generalized linear models (GLM), iteratively re-weighted least squares (IRLS) techniques, which are often used to find the maximum likelihood estimates of a GLM, can be adapted for analysis in this setting. This paper highlights the use of a Gamma-based probability transform in producing normalized residuals as model diagnostics. The approach is demonstrated for quality assurance analyses associated with physical phantom studies-recovering estimates of local bias and variance characteristics in an operational scanner. Numerical simulations show that when the Gamma assumption is reasonable, gains in efficiency are obtained. This paper shows that the adaptation of standard analysis methods to accommodate the Gamma structure is straightforward and beneficial.

Validation of a simplified scatter correction method for 3D brain PET with 15O

Objective

Positron emission tomography (PET) enables quantitative measurements of various biological functions. Accuracy in data acquisition and processing schemes is a prerequisite for this. The correction of scatter is especially important when a 3D PET scanner is used. The aim of this study was to validate the use of a simplified calculation-based scatter correction method for ¹⁵O studies in the brain.

Methods

We applied two scatter correction methods to the same ¹⁵O PET data acquired from patients with cerebrovascular disease (n = 10): a hybrid dual-energy-window scatter correction (reference method), and a deconvolution scatter correction (simplified method). The PET study included three sequential scans for ¹⁵O-CO, ¹⁵O-O₂, and ¹⁵O-H₂O, from which the following quantitative parameters were calculated, cerebral blood flow, cerebral blood volume, cerebral metabolic rate of oxygen, and oxygen extraction fraction.

Results

Both scatter correction methods provided similar reconstruction images with almost identical image noise, although there were slightly greater differences in white-matter regions compared with gray matter regions. These differences were also greater for ¹⁵O-CO than for ¹⁵O-H₂O and ¹⁵O-O₂. Region of interest analysis of the quantitative parameters demonstrated that the differences were less than 10 % (except for cerebral blood volume in white-matter regions), and the agreement between the methods was excellent, with intraclass correlation coefficients above 0.95 for all the parameters.

Conclusions

The deconvolution scatter correction despite its simplified implementation provided similar results to the hybrid dual-energy-window scatter correction. We consider it suitable for application in a clinical ¹⁵O brain study using a 3D PET scanner.