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This paper is concerned with the quantitative analysis of multicomponent mixtures by diffuse reflectance spectroscopy. Near-infrared reflectance (NIRR) measurements are related to chemical composition but in a nonlinear way, and light scatter distorts the data. Various response linearizations of reflectance (R) are compared ( R with Saunderson correction for internal reflectance, log 1/ R, and Kubelka-Munk transformations and its inverse). A multi-wavelength concept for optical correction (Multiplicative Scatter Correction, MSC) is proposed for separating the chemical light absorption from the physical light scatter. Partial Least Squares (PLS) regression is used as the multivariate linear calibration method for predicting fat in meat from linearized and scatter-corrected NIRR data over a broad concentration range. All the response linearization methods improved fat prediction when used with the MSC; corrected log 1/ R and inverse Kubelka-Munk transformations yielded the best results. The MSC provided simpler calibration models with good correspondence to the expected physical model of meat. The scatter coefficients obtained from the MSC correlated with fat content, indicating that fat affects the NIRR of meat with an additive absorption component and a multiplicative scatter component.

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SUMMARYThe Lohmoller-Wold decomposition of multi-way (three-way, four-way, etc.) data arrays is combined with the non-linear partial least squares (NIPALS) algorithms to provide multi-way solutions of principal components analysis (PCA) and partial least squares modelling in latent variables (PLS).The decomposition of a multi-way array is developed as the product of a score vector and a loading array, where the score vectors have the same properties as those of ordinary two-way PCA and PLS. In image analysis, the array would instead be decomposed as the product of a loading vector and an image score matrix. The resulting methods are equivalent to the method of unfolding a multi-way array to a two-way matrix followed by ordinary PCA or PLS analysis. This automatically proves the eigenvector and least squares properties of the multi-way PCA and PLS methods.The methodology is presented; the algorithms are outlined and illustrated with a small chemical example.

Multivariate image analysis (MIA) is a methodology for analyzing multivariate images, where the image coordinates are position (two‐ or three‐dimensions) and variable number. Multivariate images can have typical sizes 1024 × 1024, 512 × 512, 256 × 256 etc. and have between two and many hundreds of variables. The variables can be wavelength, electron energy, particle mass and many others. Image analysis concentrates mainly on spatial relationships between pixels in a grey level image. MIA concentrates on the correlation of structure between the variables to provide extra information useful for exploring images and classifying regions in them. The many variables can be transformed into a few latent variable images containing condensed information. The sheer size of the data arrays necessitates visualization of raw data, intermediate data and analysis results. All physical techniques for measuring materials can be made into imaging techniques, describing not only a property, but also its position in a plane or volume. All imaging techniques can be expanded to become multivariate. Multivariate imaging is used in three major fields: remote sensing, medical imaging and microscopy (including macroscopy). In microscopy it can be used to study materials and biological processes by optical, electron and charged particle techniques.

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