Log-Gaussian gamma processes for training Bayesian neural networks in Raman and CARS spectroscopies.

We propose an approach utilizing gamma-distributed random variables, coupled with log-Gaussian modeling, to generate synthetic datasets suitable for training neural networks. This addresses the challenge of limited real observations in various applications. We apply this methodology to both Raman and coherent anti-Stokes Raman scattering (CARS) spectra, using experimental spectra to estimate gamma process parameters. Parameter estimation is performed using Markov chain Monte Carlo methods, yielding a full Bayesian posterior distribution for the model which can be sampled for synthetic data generation. Additionally, we model the additive and multiplicative background functions for Raman and CARS with Gaussian processes. We train two Bayesian neural networks to estimate parameters of the gamma process which can then be used to estimate the underlying Raman spectrum and simultaneously provide uncertainty through the estimation of parameters of a probability distribution. We apply the trained Bayesian neural networks to experimental Raman spectra of phthalocyanine blue, aniline black, naphthol red, and red 264 pigments and also to experimental CARS spectra of adenosine phosphate, fructose, glucose, and sucrose. The results agree with deterministic point estimates for the underlying Raman and CARS spectral signatures.

Bayesian Quantification for Coherent Anti-Stokes Raman Scattering Spectroscopy.

We propose a Bayesian statistical model for analyzing coherent anti-Stokes Raman scattering (CARS) spectra. Our quantitative analysis includes statistical estimation of constituent line-shape parameters, the underlying Raman signal, the error-corrected CARS spectrum, and the measured CARS spectrum. As such, this work enables extensive uncertainty quantification in the context of CARS spectroscopy. Furthermore, we present an unsupervised method for improving spectral resolution of Raman-like spectra requiring little to no a priori information. Finally, the recently proposed wavelet prism method for correcting the experimental artifacts in CARS is enhanced by using interpolation techniques for wavelets. The method is validated using CARS spectra of adenosine mono-, di-, and triphosphate in water, as well as equimolar aqueous solutions of d-fructose, d-glucose, and their disaccharide combination sucrose.