Open Access
December 2018 Standardization of multivariate Gaussian mixture models and background adjustment of PET images in brain oncology
Meng Li, Armin Schwartzman
Ann. Appl. Stat. 12(4): 2197-2227 (December 2018). DOI: 10.1214/18-AOAS1149


In brain oncology, it is routine to evaluate the progress or remission of the disease based on the differences between a pre-treatment and a post-treatment Positron Emission Tomography (PET) scan. Background adjustment is necessary to reduce confounding by tissue-dependent changes not related to the disease. When modeling the voxel intensities for the two scans as a bivariate Gaussian mixture, background adjustment translates into standardizing the mixture at each voxel, while tumor lesions present themselves as outliers to be detected. In this paper, we address the question of how to standardize the mixture to a standard multivariate normal distribution, so that the outliers (i.e., tumor lesions) can be detected using a statistical test. We show theoretically and numerically that the tail distribution of the standardized scores is favorably close to standard normal in a wide range of scenarios while being conservative at the tails, validating voxelwise hypothesis testing based on standardized scores. To address standardization in spatially heterogeneous image data, we propose a spatial and robust multivariate expectation-maximization (EM) algorithm, where prior class membership probabilities are provided by transformation of spatial probability template maps and the estimation of the class mean and covariances are robust to outliers. Simulations in both univariate and bivariate cases suggest that standardized scores with soft assignment have tail probabilities that are either very close to or more conservative than standard normal. The proposed methods are applied to a real data set from a PET phantom experiment, yet they are generic and can be used in other contexts.


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Meng Li. Armin Schwartzman. "Standardization of multivariate Gaussian mixture models and background adjustment of PET images in brain oncology." Ann. Appl. Stat. 12 (4) 2197 - 2227, December 2018.


Received: 1 November 2016; Revised: 1 January 2018; Published: December 2018
First available in Project Euclid: 13 November 2018

zbMATH: 07029452
MathSciNet: MR3875698
Digital Object Identifier: 10.1214/18-AOAS1149

Keywords: Background adjustment , multivariate Gaussian mixture model , outlier detection , PET images , robust EM algorithm , spatial modeling , standardized scores , tail distributions , tumor detection , voxelwise inference

Rights: Copyright © 2018 Institute of Mathematical Statistics

Vol.12 • No. 4 • December 2018
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