Analyzing Raman Spectral Data without Separabiliy Assumption
- 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.
Author: | Konstantin FackeldeyORCiD, Jonas Röhm, Amir Niknejad, Surahit ChewleORCiD, Marcus Weber |
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Document Type: | Article |
Parent Title (German): | Journal of Mathematical Chemistry |
Volume: | 3 |
Issue: | 59 |
First Page: | 575 |
Last Page: | 596 |
Publisher: | Springer |
Year of first publication: | 2021 |
ArXiv Id: | http://arxiv.org/abs/2007.06428 |
DOI: | https://doi.org/10.1007/s10910-020-01201-7 |