Effect of non-resonant background on the extraction of Raman signals from CARS spectra using deep neural networks

PhAI: A deep-learning approach to solve the crystallographic phase problem

X-ray crystallography provides a distinctive view on the three-dimensional structure of crystals. To reconstruct the electron density map, the complex structure factors [Formula: see text] of a sufficiently large number of diffracted reflections must be known. In a conventional experiment, only the amplitudes [Formula: see text] are obtained, and the phases ϕ are lost. This is the crystallographic phase problem. In this work, we show that a neural network, trained on millions of artificial structure data, can solve the phase problem at a resolution of only 2 angstroms, using only 10 to 20% of the data needed for direct methods. The network works in common space groups and for modest unit-cell dimensions and suggests that neural networks could be used to solve the phase problem in the general case for weakly scattering crystals.

Estimation of biological variance in coherent Raman microscopy data of two cell lines using chemometrics

Broadband Coherent Anti-Stokes Raman Scattering (BCARS) is a valuable spectroscopic imaging tool for visualizing cellular structures and lipid distributions in biomedical applications. However, the inevitable biological changes in the samples (cells/tissues/lipids) introduce spectral variations in BCARS data and make analysis challenging. In this work, we conducted a systematic study to estimate the biological variance in BCARS data of two commonly used cell lines (HEK293 and HepG2) in biomedical research. The BCARS data were acquired from two different experimental setups (Leibniz Institute of Photonics Technology (IPHT) in Jena and Politecnico di Milano (POLIMI) in Milano) to evaluate the reproducibility of results. Also, spontaneous Raman data were independently acquired at POLIMI to validate those results. First, Kramers-Kronig (KK) algorithm was utilized to retrieve Raman-like signals from the BCARS data, and a pre-processing pipeline was subsequently used to standardize the data. Principal component analysis - Linear discriminant analysis (PCA-LDA) was performed using two cross-validation (CV) methods: batch-out CV and 10-fold CV. Additionally, the analysis was repeated, considering different spectral regions of the data as input to the PCA-LDA. Finally, the classification accuracies of the two BCARS datasets were compared with the results of spontaneous Raman data. The results demonstrated that the CH band region (2770-3070 cm-1) and spectral data in the 1500-1800 cm-1 region have significantly contributed to the classification. A maximum of 100% balanced accuracies were obtained for the 10-fold CV for both BCARS setups. However, in the case of batch-out CV, it is 92.4% for the IPHT dataset and 98.8% for the POLIMI dataset. This study offers a comprehensive overview for estimating biological variance in biomedical applications. The insights gained from this analysis hold promise for improving the reliability of BCARS measurements in biomedical applications, paving the way for more accurate and meaningful spectroscopic analyses in the study of biological systems.

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.