Factor Analysis of Dynamic PET Images: Beyond Gaussian Noise

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 β-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 β, 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 β to improve factor analysis.

Voxelwise Principal Component Analysis of Dynamic [S-Methyl-11C]Methionine PET Data in Glioma Patients

“…For the sake of completeness, it should be noted that other dimension reduction techniques have been proposed in the literature for the analysis of dynamic PET data, such as factor analysis of dynamic structures (FADS) and non-negative matrix factorization (NMF) [ 46 ]. These are distinguished by their ability to isolate signal from noise, which strongly depends on the assumptions made on the noise distribution in PET images.…”

“…These are distinguished by their ability to isolate signal from noise, which strongly depends on the assumptions made on the noise distribution in PET images. Whereas the noise related to the event counting in PET imaging follows a Poisson distribution, the noise distribution in reconstructed PET images is less well characterized due to alterations related to the system hardware and reconstruction algorithm—including scatter and attenuation corrections [ 46 ]—hence remains an open problem. Comparison of these methods in the particular case of dynamic [ 11 C]MET PET data of glioma patients would also be of interest as a future work.…”

Extraction of physically meaningful endmembers from STEM spectrum-images combining geometrical and statistical approaches

“…Appendix B suggests that dramatic deviation from the linear mixing model can be observed in cases when low-loss EEL spectra of constituting compounds are drastically different and TEM samples are thick. Such cases would require the application of non-linear mixing model accounting for the interaction terms in spectra formation similar to those described in [47,48,49,50,51,52,53].…”

“…5b. This is however a rather subjective prior reflecting only our believe in (52). We will construct a less subjective prior that satisfies (52) but utilises some information from counts X(i) observable in the histogram range [0, l].…”

Dynamic PET Image Reconstruction Incorporating Multiscale Superpixel Clusters

“…In the different context of post-reconstruction dynamic PET image analysis, a number of clustering-based techniques have been proposed to reduce noise in kinetic analysis. Factor analysis seeks to decompose dynamic cardiac PET images into different tissue types based on their unique temporal signatures to improve quantification of physiological function [28]- [30]. In oncologic whole-body imaging, the principal component analysis (PCA) approach has been used to enhance the distinction of tumors in dynamic FDG images compared with conventional static standard uptake value (SUV) images [31].…”