Analysis of Infrared and Raman Imaging Data Using Alternating and Modified Alternating Least Squares

Abstract

Modified alternating least squares (MALS) outperforms alternating least squares (ALS) in the analysis of infrared and Raman image spectral data. MALS offers superior stability thanks to ridge regression and a substantial speed advantage due to the kernel nature of the algorithm, reducing computational overhead. MALS excels in resolving basis vectors even in low signal-to-noise, nearly collinear data, whereas ALS often falls short. For spectroscopic imaging, both MALS and other ALS methods rely on spatial resolution between sample components, as low spatial resolution leads to increased mixing of components. Spectroscopic imaging combines spectroscopy and digital imaging to extract chemical composition. Multivariate curve resolution (MCR)’s foundation in ALS regression makes it a vital tool for this analysis, enabling a comprehensive examination of complex spectroscopic images. This tutorial delves into the mathematical techniques necessary for extracting chemical insights from infrared and Raman spectroscopic images. While this discussion focuses on two-dimensional spatial data, the methodology can be extended to three-dimensional data.