Exploiting spatial‐domain simplicity in spectral image analysis

Abstract

AbstractFull‐spectrum imaging is fast becoming a tool of choice for characterizing heterogeneous materials. Spectral images, which consist of a complete spectrum at each point in a spatial array, can be acquired from a wide variety of surface and microanalytical spectroscopic techniques. It is not uncommon that such spectral image data sets comprise tens of thousands of individual spectra, or more. Given the vast quantities of raw spectral data, factor analysis methods have proved indispensable for extracting the chemical information from these high‐dimensional data sets into a limited number of factors that represent the spectral and spatial characteristics of the sample's composition. It is well known that factor models suffer a ‘rotational ambiguity’, that is, there are an infinite number of factor models that will fit the data equally well. Thus, physically inspired constraints are often employed to derive relatively unique models that make the individual factors more easily interpreted by the practicing analyst. In the present work, we note that many samples undergoing spectral image analysis are ‘simple’ in the sense that only one or a few of the sample's constituents are present at any particular location. When this situation prevails, simplicity in the spatial domain can be exploited to make the resulting factor models more realistic. In particular, orthogonal rotation of the spatial‐domain vectors arising from singular value decomposition (SVD) of the spectral data matrix will be shown to be an effective method for making physically acceptable and easily interpretable estimates of the pure‐component spectra and abundances. Copyright © 2009 John Wiley & Sons, Ltd.