Analyzing Raman Spectral Data without Separability Assumption

TL;DR

This paper introduces a novel method for analyzing Raman spectral data that does not rely on the separability assumption, improving the analysis of complex chemical spectra in time-resolved experiments.

Contribution

The paper presents a new approach for matrix factorization in Raman spectroscopy that removes the need for the separability assumption, enhancing analysis capabilities.

Findings

Effective on real-world chemical data

Outperforms traditional methods under non-separable conditions

Demonstrates robustness in time-resolved spectroscopy

Abstract

Raman spectroscopy is a well established tool for the analysis of vibration spectra, which then allow for the determination of individual substances in a chemical sample, or for their phase transitions. In the Time-Resolved-Raman-Sprectroscopy the vibration spectra of a chemical sample are recorded sequentially over a time interval, such that conclusions for intermediate products (transients) can be drawn within a chemical process. The observed data-matrix $M$ from a Raman spectroscopy can be regarded as a matrix product of two unknown matrices $W$ and $H$, where the first is representing the contribution of the spectra and the latter represents the chemical spectra. One approach for obtaining $W$ and $H$ is the non-negative matrix factorization. We propose a novel approach, which does not need the commonly used separability assumption. The performance of this approach is shown on a real world chemical example.