Gaussian process analysis of electron energy loss spectroscopy data: multivariate reconstruction and kernel control

Advances in hyperspectral imaging including electron energy loss spectroscopy bring forth the challenges of exploratory and physics-based analysis of multidimensional data sets. The multivariate linear unmixing methods generally explore similarities in the energy dimension, but ignore correlations in the spatial domain. At the same time, Gaussian process (GP) explicitly incorporate spatial correlations in the form of kernel functions but is computationally intensive. Here, we implement a GP method operating on the full spatial domain and reduced representations in the energy domain. In this multivariate GP, the information between the components is shared via a common spatial kernel structure, while allowing for variability in the relative noise magnitude or image morphology. We explore the role of kernel constraints on the quality of the reconstruction, and suggest an approach for estimating them from the experimental data. We further show that spatial information contained in higher-order components can be reconstructed and spatially localized.

Automated summary

Advances in hyperspectral imaging, including electron energy loss spectroscopy, present challenges in exploratory and physics-based analysis of multidimensional data sets. While multivariate linear unmixing methods explore similarities in the energy dimension, Gaussian process methods explicitly incorporate spatial correlations but are computationally intensive. Researchers implemented a Gaussian process method that operates on the full spatial domain and reduced representations in the energy domain, sharing information between components via a common spatial kernel structure and suggesting an approach for estimating kernel constraints from experimental data to improve reconstruction quality.