Model-Fitting Weighted Least Squares as an Alternative to Principal Component Analysis for Analyzing Energy-Dispersive X-ray Spectroscopy Spectrum Images

Abstract

Spectrum imaging with energy-dispersive X-ray spectroscopy (EDS) has become ubiquitous in material characterization using electron microscopy. Multivariate statistical methods, commonly principal component analysis (PCA), are often used to aid analysis of the resulting multidimensional datasets; PCA can provide denoising prior to further analysis or grouping of pixels into distinct phases with similar signals. However, it is well known that PCA can introduce artifacts at low signal-to-noise ratios. Unfortunately, when evaluating the benefits and risks with PCA, it is often compared only against raw data, where it tends to shine; alternative data analysis methods providing a fair point of comparison are often lacking. Here, we directly compare PCA with a strategy based on (the conceptually and computationally simpler) weighted least squares (WLS). We show that for four representative cases, model fitting of the sum spectrum followed by WLS (mfWLS) consistently outperforms PCA in terms of finding and accurately describing compositional gradients and inclusions and as a preprocessing step to clustering. Additionally, we demonstrate that some common artifacts and biases displayed by PCA are avoided with the mfWLS approach. In summary, mfWLS can provide a superior option to PCA for analysis of EDS spectrum images as the signal is simply and accurately modeled.