Hyperspectral unmixing for Raman spectroscopy via physics-constrained autoencoders

TL;DR

This work introduces a framework for Raman unmixing based on autoencoder neural networks and demonstrates that such methods offer more versatile, robust, and data-driven Raman unmixing with improved performance compared to conventional methods in complex samples.

Abstract

Raman spectroscopy is widely used across scientific domains to characterize the chemical composition of samples in a non-destructive, label-free manner. Many applications entail the unmixing of signals from mixtures of molecular species to identify the individual components present and their proportions, yet conventional methods for chemometrics often struggle with complex mixture scenarios encountered in practice. Here, we develop hyperspectral unmixing algorithms based on autoencoder neural networks, and we systematically validate them using both synthetic and experimental benchmark datasets created in-house. Our results demonstrate that unmixing autoencoders provide improved accuracy, robustness and efficiency compared to standard unmixing methods. We also showcase the applicability of autoencoders to complex biological settings by showing improved biochemical characterization of volumetric Raman imaging data from a monocytic cell.

Figures (10)

• Figure 1: Hyperspectral unmixing for Raman spectroscopy using autoencoder neural networks.a, Diagram of the task of hyperspectral unmixing. b, Hyperspectral unmixing as a self-supervised autoencoder learning problem: the decoder learns to derive endmembers and the encoder learns the corresponding fractional abundances. c, Encoders can accommodate different concepts from representation learning, such as convolutional layers and attention, to improve feature extraction and provide more accurate and robust unmixing. d, Decoders can be structured to model different linear and non-linear mixing models. Labels in red in c and d indicate physics-inspired constraints.
• Figure 2: Benchmarking autoencoders on synthetic Raman mixtures.a, Schematic of our synthetic data generation workflow. b, Representative results for the six algorithms (two conventional and four AEs) on an example synthetic dataset (Chessboard+artifacts scenario): endmembers (left), and fractional abundances (right). c-d, Summary of unmixing performance on synthetic datasets of variable mixing level and complexity: linear mixtures (c), bilinear mixtures (d). Confidence intervals are given by one standard deviation around the sample mean ($n=25$ samples: $5$ datasets with $5$ model repetitions each).
• Figure 3: Computational efficiency of autoencoders and conventional methods on synthetic datasets with an increasing number of spectra. Each dot represents the average across 3 evaluations (confidence intervals based on one standard deviation are small and not visible to the eye). AE models are equipped with decoders for linear unmixing. Data generated under Chessboard +artifacts.
• Figure 4: Experimental validation on Raman spectroscopy data from sugar solutions.a, Schematic diagram of sugar mixture preparation. Two sets of data are acquired---high and low signal-to-noise ratio (SNR) data, by using integration times of 5 and 0.5, respectively. b, Endmember signatures estimated from reference spectra (high SNR) additionally collected from pure solutions. c-d, Summary of unmixing performance for: c, idealized scenario with augmented data including reference spectra; and d, original data without augmentation. Confidence intervals are given as one standard deviation around the sample mean ($n=5$).
• Figure 5: Analysis of volumetric Raman imaging of a THP-1 cell with unmixing autoencoders.a, A brightfield image of the studied THP-1 cell. b, A cross-section reconstruction of the cell (layer $z=7$) obtained by overlaying the fractional abundances derived by: VCA+NNLS, our Dense AE, and a deeper Dense AE. c, Results obtained with our deeper Dense AE model, displaying the spatial distribution of the individual fractional abundances and the associated endmember signatures. Fractional abundance maps normalized for consistent visualization. Data from Kallepitis et al.kallepitis2017quantitative.