Assessment of essential information in the Fourier domain to accelerate Raman hyperspectral microimaging

In the context of multivariate curve resolution (MCR) and spectral unmixing, essential information (EI) corresponds to the most linearly dissimilar rows or/and columns of a two-way data matrix. These rows/columns are called essential because they are indispensable to reproduce the full data matrix in a convex linear way. The selection of EI is driven by the properties of linear spectral mixtures. In recent works, it has been revealed to be a very useful practical tool to select the most relevant spectral information before MCR analysis, key features being speed and compression ability. However, the canonical approach relies on principal component analysis (PCA) to evaluate the convex hull that encapsulates the data structure in the normalized score space. This implies that the evaluation of the essentiality of each spectrum can only be achieved after all the spectra have been acquired by the instrument. This paper proposes a new approach, denominated EIFD, which consists in extracting EI in the Fourier domain. Spectral information is transformed into Fourier coefficients and EI is assessed from a convex hull analysis of the data point cloud in the 2D phasor plots of the first few harmonics. The proposed EIFD approach is broadly applicable and very efficient in terms of spectral compression and denoising. In particular, it has the crucial advantage that the coordinate system of a phasor plot does not depend on the data themselves. This enables dynamic (i.e., performed during data acquisition) and chemometric-driven (i.e., based on spectral relevance for unmixing) selective sampling. The usefulness of EIFD is shown by analyzing Raman hyperspectral microimaging data, demonstrating the possibility of a 50-fold acceleration of Raman acquisition.