Unmixing Dynamic Pet Images: Combining Spatial Heterogeneity and Non-gaussian Noise

Abstract

An important task when processing dynamic PET images is to identify the time-activity curves (TACs) of the pure tissues, along with their corresponding spatial proportions. This step, often referred to as unmixing or factor analysis, is based on a loss function which measures the discrepancy between the observed data and the model. This loss function should be chosen according to the statistical properties of the noise, which is in this case hard to characterize. Indeed, while dynamic PET images results from a decay process that can be statistically described by a Poisson distribution, acquisition and post-filtering reconstruction drastically change the nature of the noise. In the literature dedicated to factor analysis of dynamic PET images, a common and underlying assumption consists in assuming that the dynamic PET images are corrupted by an additive Gaussian or by a Poisson noise. These assumptions lead to the choice of the squared Euclidian distance and the Kullback-Leibler divergence. We propose here to consider the β-divergence, which is able to encompass a wide family of divergence measures corresponding to various noise distributions. This loss function is incorporated into three different factor models and evaluated using four sets of synthetic data.