  Advances in hyperspectral imaging modes including electron energy loss
spectroscopy (EELS) in scanning transmission electron microscopy (STEM) bring
forth the challenges of exploratory and subsequently physics-based analysis of
multidimensional data sets. The (by now common) multivariate unsupervised
linear unmixing methods and their nonlinear analogs generally explore
similarities in the energy dimension but ignore correlations in the spatial
domain. At the same time, Gaussian process (GP) methods that explicitly
incorporate spatial correlations in the form of kernel functions tend to be
extremely computationally intensive, while the use of inducing point-based
sparse methods often leads to reconstruction artefacts. Here, we suggest and
implement a parallel GP method operating on the full spatial domain and reduced
representations in the energy domain. In this parallel 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 common spatial structures and kernel constraints on the
quality of the reconstruction and suggest an approach for estimating these
factors from the experimental data. Application of this method to an example
EELS dataset demonstrates that spatial information contained in higher-order
components can be reconstructed and spatially localized. This approach can be
further applied to other hyperspectral and multimodal imaging modes. The
notebooks developed in this manuscript are freely available as part of a GPim
package (https://github.com/ziatdinovmax/GPim).
