在没有可分离性假设的情况下分析拉曼光谱数据
Analyzing Raman Spectral Data without Separability Assumption
摘要：
拉曼光谱是用于分析振动光谱的成熟工具，然后允许确定化学样品中的单个物质或其相变。在时间分辨拉曼光谱中，化学样品的振动光谱在一段时间间隔内被连续记录，从而可以得出化学过程中中间产物（瞬态）的结论。从拉曼光谱中观察到的数据矩阵$M$可以被认为是两个未知矩阵$W$和$H$的矩阵乘积，其中第一个表示光谱的贡献，而后者表示化学光谱。用于获得$W$和$H$的一种方法是非负矩阵因式分解。我们提出了一种新的方法，它不需要常用的可分性假设。这种方法的性能显示在一个现实世界的化学例子。
英文摘要：
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.
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