On-the-fly spectral unmixing based on Kalman filtering

TL;DR

This paper presents an innovative online spectral unmixing method using Kalman filtering that efficiently analyzes spectral data in real-time, reducing computational load while maintaining accuracy, suitable for dynamic applications like microscopy.

Contribution

It introduces the first real-time spectral unmixing approach based on Kalman filtering that operates in a lower-dimensional subspace with nonnegativity constraints.

Findings

Effective in synthetic and real Raman datasets

Balances unmixing accuracy and computational efficiency

Operates in a lower-dimensional subspace for speed

Abstract

This work introduces an on-the-fly (i.e., online) linear unmixing method which is able to sequentially analyze spectral data acquired on a spectrum-by-spectrum basis. After deriving a sequential counterpart of the conventional linear mixing model, the proposed approach recasts the linear unmixing problem into a linear state-space estimation framework. Under Gaussian noise and state models, the estimation of the pure spectra can be efficiently conducted by resorting to Kalman filtering. Interestingly, it is shown that this Kalman filter can operate in a lower-dimensional subspace while ensuring the nonnegativity constraint inherent to pure spectra. This dimensionality reduction allows significantly lightening the computational burden, while leveraging recent advances related to the representation of essential spectral information. The proposed method is evaluated through extensive numerical experiments conducted on synthetic and real Raman data sets. The results show that this Kalman filter-based method offers a convenient trade-off between unmixing accuracy and computational efficiency, which is crucial for operating in an on-the-fly setting. To the best of the authors' knowledge, this is the first operational method which is able to solve the spectral unmixing problem efficiently in a dynamic fashion. It also constitutes a valuable building block for benefiting from acquisition and processing frameworks recently proposed in the microscopy literature, which are motivated by practical issues such as reducing acquisition time and avoiding potential damages being inflicted to photosensitive samples.