High spatial resolution hyperspectral imaging with machine-learning techniques

Recent advances in scanning transmission electron microscopy (STEM) techniques have enabled us to obtain spectroscopic datasets such as those generated by electron energy-loss (EELS)/energy-dispersive X-ray (EDX) spectroscopy measurements in a PC-controlled way from a specified region of interest (ROI) even at atomic scale resolution, also known as hyperspectral imaging (HSI). Instead of conventional analytical procedures, in which the potential constituent chemical components are manually identified and the chemical state of each spectral component is successively determined, a statistical machine-learning approach, which is known to be more effective and efficient for the automatic resolution and extraction of the underlying chemical components stored in a huge three-dimensional array of an observed HSI dataset, is used. Among the statistical approaches suitable for processing HSI datasets, methods based on matrix factorization such as principal component analysis (PCA), multivariate curve resolution (MCR), and nonnegative matrix factorization (NMF) are useful to find an essential low-dimensional data subspace hidden in the HSI dataset. This chapter describes our developed NMF method, which has two additional terms in the objective function, and which is particularly effective for analyzing STEM-EELS/EDX HSI datasets: (i) a soft orthogonal penalty, which clearly resolves partially overlapped spectral components in their spatial distributions and (ii) an automatic relevance determination (ARD) prior, which optimizes the number of components involved in the observed data. Our analysis of real STEM-EELS/EDX HSI datasets demonstrates that the soft orthogonal penalty is effective to obtain the correct decomposition and that the ARD prior successfully identifies the correct number of physically meaningful components.