Enhanced Raman hyperspectral imaging using RS-NMF: a novel Regularized Sparse Non-negative Matrix Factorization for spectral unmixing

Molecular spectroscopy is a powerful, non-destructive technique for chemical analysis, as the sample remains unaltered during the measurement. Although it is essential for getting meaningful information, it often suffers from spectral overlap, making it challenging to identify individual components within a sample. Therefore, for over fifty years, a plethora of mathematical approaches have been developed to unmix complex signals and push the detection limits of spectroscopic instruments, such as Blind Source Separation (BSS) or Multivariate Curve Resolution (MCR), to name but a few. However, despite these numerous advances, and even as the amount of data increases – potentially providing more information – they continue to face inherent limitations (i.e., selectivity problems), particularly when dealing with contemporary samples, making their thorough characterization an increasingly intricate challenge, especially with diminishing prior knowledge. This article presents a novel signal unmixing method applied to hyperspectral Raman imaging designed to overcome these limitations. Our approach, based on a Non-Negative Matrix Factorization (NMF), addresses critical challenges such as rotational ambiguity and noise sensitivity, which often prevent accurate pure component spectral unmixing. First, we introduce our methodology and explain how it differs from existing mathematical methods. We then evaluate its performance on a well-known real-world dataset in the chemometrics community called “emulsion” from hyperspectral Raman imaging. To further challenge our method, we apply it to a complex simulated molecular signal dataset. Finally, we compare our results with those obtained using the standard MCR-ALS approach. Our initial results demonstrate that this RS-NMF approach improves the unmixing of complex signals.