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

Abstract

Access to the full text of the published version may require a subscription. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. The Gamma Characteristic of Reconstructed PET Images: Implications for ROI Analysis. Rights Tian Mou, Jian Huang and Finbarr O'SullivanAbstract-The basic emission process associated with 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 expectationmaximization (EM), widely used in clinical imaging now, impose positivity constraints that impact noise properties. The present work is motivated by 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 inferencemodel 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. Our work 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. The work shows that the adaptation of standard analysis methods to accommodate the Gamma structure is straightforward and beneficial.

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“…Obviously, model (2) reduces to model (1) , when the transform Q does not vary with κ . If Q (·∣ κ ) corresponded to a scaled Gamma distribution then, based on ( Mou et al, 2017 ), κ would increase with dose or sensitivity. And with increasing κ , Q becomes linear.…”