A multiscale Bayesian approach to quantification and denoising of energy-dispersive x-ray data

Energy dispersive X-ray (EDX) spectrum imaging yields compositional information with a
spatial resolution down to the atomic level. However, experimental limitations often
produce extremely sparse and noisy EDX spectra. Under such conditions, every detected
X-ray must be leveraged to obtain the maximum possible amount of information about
the sample. To this end, we introduce a robust multiscale Bayesian approach that
accounts for the Poisson statistics in the EDX data and leverages their underlying spatial
correlations. This is combined with EDX spectral simulation (elemental contributions
and Bremsstrahlung background) into a Bayesian estimation strategy. When tested using
simulated datasets, the chemical maps obtained with this approach are more accurate
and preserve a higher spatial resolution than those obtained by standard methods. These
properties translate to experimental datasets, where the method enhances the atomic
resolution chemical maps of a canonical tetragonal ferroelectric PbTiO3 sample, such
that ferroelectric domains are mapped with unit-cell resolution.