A comparison of noise models in a hybrid reference spectrum and principal components analysis algorithm for Raman spectroscopy

Raman spectroscopy exploits the Raman scattering effect to analyze chemical compounds with the use of laser light. Raman spectra are most commonly analyzed using the ordinary least squares (LS) method. However, LS is known to be sensitive to variability in the spectra of the analyte and background materials. In a previous paper, we addressed this problem by proposing a novel algorithm that models expected variations in the analyte as well as background signals. The method was called the hybrid LS and principal component analysis (HLP) algorithm and used an unweighted Gaussian distribution to model the noise in the measured spectra. In this paper, we show that the noise in fact follows a Poisson distribution and improve the noise model of our hybrid algorithm accordingly. We also approximate the Poisson noise model by a weighted Gaussian noise model, which enables the use of a more efficient solver algorithm. To reflect the generalization of the noise model, we from hereon call the method the hybrid reference spectrum and principal components analysis (HRP) algorithm. We compare the performance of LS and HRP with the unweighted Gaussian (HRP-G), Poisson (HRP-P), and weighted Gaussian (HRP-WG) noise models. Our experiments use both simulated data and experimental data acquired from a serial dilution of Raman-enhanced gold-silica nanoparticles placed on an excised pig colon. When the only signal variability was zero-mean random noise (as examined using simulated data), HRP-P consistently outperformed HRP-G and HRP-WG, with the latter coming in as a close second. Note that in this scenario, LS and HRP-G were equivalent. In the presence of random noise as well as variations in the mean component spectra, the three HRP algorithms significantly outperformed LS, but performed similarly among themselves. This indicates that, in the presence of significant variations in the mean component spectra, modeling such variations is more important than optimizing the noise model. It also suggests that for real data, HRP-WG provides a desirable trade-off between noise model accuracy and computational speed. Copyright (c) 2013 John Wiley & Sons, Ltd.