Factor analysis of dynamic PET images: beyond Gaussian noise

TL;DR

This paper explores the use of different divergence measures, especially the beta-divergence, in factor analysis of dynamic PET images to better handle complex noise characteristics beyond Gaussian assumptions.

Contribution

It introduces a framework using beta-divergence for factor analysis in PET imaging, accommodating various noise models without explicit noise distribution modeling.

Findings

Non-standard beta values improve factor analysis performance.

Different divergence measures suit different noise types.

Method tested on synthetic and real PET images.

Abstract

Factor analysis has proven to be a relevant tool for extracting tissue time-activity curves (TACs) in dynamic PET images, since it allows for an unsupervised analysis of the data. Reliable and interpretable results are possible only if considered with respect to suitable noise statistics. However, the noise in reconstructed dynamic PET images is very difficult to characterize, despite the Poissonian nature of the count-rates. Rather than explicitly modeling the noise distribution, this work proposes to study the relevance of several divergence measures to be used within a factor analysis framework. To this end, the $\beta$-divergence, widely used in other applicative domains, is considered to design the data-fitting term involved in three different factor models. The performances of the resulting algorithms are evaluated for different values of $\beta$, in a range covering Gaussian, Poissonian and Gamma-distributed noises. The results obtained on two different types of synthetic images and one real image show the interest of applying non-standard values of $\beta$ to improve factor analysis.