From STEM-EDXS data to phase separation and quantification using physics-guided NMF

Abstract

We present the development of a new algorithm which combines state-of-the-art energy-dispersive x-ray (EDX) spectroscopy theory and a suitable machine learning formulation for the hyperspectral unmixing of scanning transmission electron microscope EDX spectrum images. The algorithm is based on non-negative matrix factorization (NMF) incorporating a physics-guided factorization model. It optimizes a Poisson likelihood, under additional simplex constraint together with user-chosen sparsity-inducing and smoothing regularizations, and is based on iterative multiplicative updates. The fluorescence of x-rays is fully modeled thanks to state-of-the-art theoretical work. It is shown that the output of the algorithm can be used for a direct chemical quantification. With this approach, it is straightforward to include a priori knowledge on the specimen such as the presence or absence of certain chemical elements in some of its phases. This work is implemented within two open-source Python packages, espm and emtables, which are used here for data simulation, data analysis and quantification. Using simulated data, we demonstrate that incorporating physical modeling in the decomposition helps retrieve meaningful components from spatially and spectrally mixed phases, even when the data are very noisy. For synthetic data with a higher signal, the regularizations yield a tenfold increase in the quality of the reconstructed abundance maps compared to standard NMF. Our approach is further validated on experimental data with a known ground truth, where state-of-the art results are achieved by using prior knowledge about the sample. Our model can be generalized to any other scanning spectroscopy techniques where underlying physical modeling can be linearized.