  Low-loss electron energy loss spectroscopy (EELS) in the scanning
transmission electron microscope (STEM) probes the valence electron density and
relevant optoelectronic properties such as band gap energies and other band
structure transitions. The measured spectra can be formulated in a dielectric
theory framework, comparable to optical spectroscopies and ab-initio
simulations. Moreover, Kramers-Kronig analysis (KKA), an inverse algorithm
based on the homonym relations, can be employed for the retrieval of the
complex dielectric function (CDF). However, spurious contributions
traditionally not considered in this framework typically impact low-loss EELS
modifying the spectral shapes and precluding the correct measurement and
retrieval of the dielectric information. A relativistic KKA algorithm is able
to account for the bulk and surface radiative-loss contributions to low-loss
EELS, revealing the correct dielectric properties. Using a synthetic low-loss
EELS model, we propose some modifications on the naive implementation of this
algorithm that broadens its range of application. The robustness of the
algorithm is improved by regularization, appliying previous knowledge about the
shape and smoothness of the correction term. Additionally, our efficient
numerical integration methodology allows processing hyperspectral datasets in a
reasonable amount of time. Harnessing these abilities, we show how simultaneous
relativistic KKA processing of several spectra can share information to produce
an improved result.
