title: Sparse modeling of EELS and EDX spectral imaging data by nonnegative matrix factorization.
abstract: Advances in scanning transmission electron microscopy (STEM) techniques have enabled us to automatically obtain electron energy-loss (EELS)/energy-dispersive X-ray (EDX) spectral datasets from a specified region of interest (ROI) at an arbitrary step width, called spectral imaging (SI). Instead of manually identifying the potential constituent chemical components from the ROI and determining the chemical state of each spectral component from the SI data stored in a huge three-dimensional matrix, it is more effective and efficient to use a statistical approach for the automatic resolution and extraction of the underlying chemical components. Among many different statistical approaches, we adopt a non-negative matrix factorization (NMF) technique, mainly because of the natural assumption of non-negative values in the spectra and cardinalities of chemical components, which are always positive in actual data. This paper proposes a new NMF model with two penalty terms: (i) an automatic relevance determination (ARD) prior, which optimizes the number of components, and (ii) a soft orthogonal constraint, which clearly resolves each spectrum component. For the factorization, we further propose a fast optimization algorithm based on hierarchical alternating least-squares. Numerical experiments using both phantom and real STEM-EDX/EELS SI datasets demonstrate that the ARD prior successfully identifies the correct number of physically meaningful components. The soft orthogonal constraint is also shown to be effective, particularly for STEM-EELS SI data, where neither the spatial nor spectral entries in the matrices are sparse.
authors.affiliation: Department of Electrical, Electronic and Computer Engineering, Gifu University, 1-1, Yanagido, Gifu 501-1193, Japan. Electronic address: shiga_m@gifu-u.ac.jp.
authors.forename: Motoki
authors.initials: M
authors.lastname: Shiga
authors.affiliation: Advanced Measurement Technology Center, Institute of Materials and Systems for Sustainability, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan.
authors.forename: Kazuyoshi
authors.initials: K
authors.lastname: Tatsumi
authors.affiliation: Advanced Measurement Technology Center, Institute of Materials and Systems for Sustainability, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan.
authors.forename: Shunsuke
authors.initials: S
authors.lastname: Muto
authors.affiliation: Graduate School of Frontier Sciences, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa 277-8561, Japan; Center for Materials Research by Information Integration, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba 305-0047, Japan; Biotechnology Research Institute for Drug Discovery, National Institute of Advanced Industrial Science and Technology, 2-4-7 Aomi Koto-ku, Tokyo 135-0064, Japan.
authors.forename: Koji
authors.initials: K
authors.lastname: Tsuda
authors.affiliation: High-Voltage Electron Microscope Laboratory, Institute of Materials and Systems for Sustainability, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan.
authors.forename: Yuta
authors.initials: Y
authors.lastname: Yamamoto
authors.affiliation: Environment and Energy Materials Division, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan.
authors.forename: Toshiyuki
authors.initials: T
authors.lastname: Mori
authors.affiliation: Division of Materials Research, Institute of Materials and Systems for Sustainability, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan.
authors.forename: Takayoshi
authors.initials: T
authors.lastname: Tanji
keywords: Automatic relevance determination; Nonnegative matrix factorization; Sparse modeling; Spatial orthogonality; Spectral imaging