2015/01/06 by Yuanchang Sun, Sun, Yuanchang, Wensong Wu +3
Biochemistry, Genetics and Molecular Biology · Chemistry · Engineering · #FOS: Mathematics #Numerical Analysis (math.NA) #Remote-Sensing Image Classification #Spectroscopy Techniques in Biomedical and Chemical Research #Spectroscopy and Chemometric Analyses
paper · pdf · doi:10.48550/arxiv.1501.01218
openalex publication_date 2015/01/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Substances such as chemical compounds are invisible to human eyes, they are usually captured by sensing equipments with their spectral fingerprints. Though spectra of pure chemicals can be identified by visual inspection, the spectra of their mixtures take a variety of complicated forms. Given the knowledge of spectral references of the constituent chemicals, the task of data fitting is to retrieve their weights, and this usually can be obtained by solving a least squares problem. Complications occur if the basis functions (reference spectra) may not be used directly to best fit the data. In fact, random distortions (spectral variability) such as shifting, compression, and expansion have been observed in some source spectra when the underlying substances are mixed. In this paper, we formulate mathematical model for such nonlinear effects and build them into data fitting algorithms. If minimal knowledge of the distortions is available, a deterministic approach termed \it augmented least squares is developed and it fits the spectral references along with their derivatives to the mixtures. If the distribution of the distortions is known a prior, we consider to solve the problem with maximum likelihood estimators which incorporate the shifts into the variance matrix. The proposed methods are substantiated with numerical examples including data from Raman spectroscopy (RS), nuclear magnetic resonance (NMR), and differential optical absorption spectroscopy (DOAS) and show satisfactory results.