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In brain oncology, it is routine to evaluate the progress or remission of thedisease based on the differences between a pre-treatment and a post-treatmentPositron Emission Tomography (PET) scan. Background adjustment is necessary toreduce confounding by tissue-dependent changes not related to the disease. Whenmodeling the voxel intensities for the two scans as a bivariate Gaussianmixture, background adjustment translates into standardizing the mixture ateach 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 astandard multivariate normal distribution, so that the outliers (i.e., tumorlesions) can be detected using a statistical test. We show theoretically andnumerically that the tail distribution of the standardized scores is favorablyclose to standard normal in a wide range of scenarios while being conservativeat the tails, validating voxelwise hypothesis testing based on standardizedscores. To address standardization in spatially heterogeneous image data, wepropose a spatial and robust multivariate expectation-maximization (EM)algorithm, where prior class membership probabilities are provided bytransformation of spatial probability template maps and the estimation of theclass mean and covariances are robust to outliers. Simulations in bothunivariate and bivariate cases suggest that standardized scores with softassignment have tail probabilities that are either very close to or moreconservative than standard normal. The proposed methods are applied to a realdata set from a PET phantom experiment, yet they are generic and can be used inother contexts.

Standardization of multivariate Gaussian mixture models and background adjustment of PET images in brain oncology