Comparison of Gaussian and Poisson noise models in a hybrid reference spectrum and principal component analysis algorithm for Raman spectroscopy

Abstract

Raman spectra are most commonly analyzed using the ordinary least squares (LS) method. However, LS is sensitive to variability in the spectra of the analyte and background materials. We previously addressed this problem by successfully proposing a novel hybrid least squares and principal components (HLP) algorithm. HLP extended LS by allowing the reference spectra to vary in accordance with the principal components observed in calibration sets. Previously, HLP assumed zero-mean Gaussian measurement noise. In this work, we show that the noise in fact follows a Poisson distribution, and update the mathematical framework of our algorithm accordingly. Since the name ’least squares’ referred to the Gaussian noise model, we also generalize the name of our algorithm to the Hybrid reference Spectrum and Principal component analysis (HSP) algorithm. The performance of the Gaussian and Poisson noise models is compared using both simulated and measured spectra. The simulated spectra were computed by adding various concentrations of Raman-enhanced gold-silica nanoparticles to three different backgrounds (paraffin, glass and quartz). The measured spectra were acquired from a serial dilution of gold-silica nanoparticles placed on an excised pig colon. For the simulated spectra, the Poisson model consistently outperformed the Gaussian model, on average reducing the mean absolute concentration error as well as its standard deviation by ~15-20%. For the measured data, the Gaussian and Poisson noise models yielded similar concentration estimates. Both HSP algorithms also outperformed the LS algorithm, indicating that the incorporation of the principal components yields a larger improvement in accuracy than the optimization of the noise model. Further comparison between the two HSP algorithms (with Gaussian and Poisson noise models) was precluded by a lack of precise ground truth knowledge of the nanoparticle concentrations on the colon tissue. However, the simulation results already demonstrated that the optimization of noise models can improve the detection accuracy of Raman spectroscopy, and that it may therefore be an important consideration in future high-sensitivity Raman imaging studies.