Curve resolution for multivariate images with applications to TOF-SIMS and Raman

Abstract Multivariate curve resolution (MCR) is a powerful technique for extracting chemical information from multivariate images (MI). Two problems with MI are (1) initializing the MCR decomposition and (2) lack of selectivity in the image. Methods derived for initializing MCR with evolving data that are naturally ordered in time are not generally applicable for MI. Purity-based methods show promise and a simple, robust purity-based algorithm has been developed to initialize the MCR decomposition. This method used distance measures to find samples (or variables) on the exterior of a data set. Lack of selectivity, common in MI, generally results in a rotational ambiguity in factors extracted with MCR. Functional constraints were tested as a means to reduce this ambiguity, and the method tested showed that functional constraints could be used to account for offsets and backgrounds in Raman images. Robust initialization and introduction of functional constraints tested here are necessary steps towards the final objective of providing a simple methodology for constraining factors in a general fashion so that knowledge of the physics and chemistry can be easily incorporated in to any MCR decomposition. Additionally, the use of a sequential decomposition method (sequential MCR) is employed to help reduce mixing of recovered components in rotationally ambiguous systems.

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