The hierarchical multivariate curve resolution (MCR) methodology of Fauteux-Lefebvre, Lavoie and Gosselin (Analytical Chemistry, 2018) blindly identifies compounds and maps their spatial distribution in spectral images by recursively decomposing the image into pixel subgroups and resolving each subgroup with a Poisson-noise-aware MCR engine, but its decisive inputs — the hierarchical stopping criteria (maximum number of levels and minimum pixel size per subgroup), the number of pure components K, and the PCA-score selection of the final spectral signatures — are chosen manually by the analyst, and the original demonstration was limited to simulated energy-dispersive X-ray spectroscopy (EDXS) data with three chemical elements. The open problem is to make this blind-analysis workflow operator-independent: establish an automated procedure that determines these parameters from the data itself, and demonstrate it beyond the original demonstration's conditions — other spectroscopic modalities (e.g., Raman, near-infrared), samples with a truly unknown number of species, many overlapping peaks, or nonlinear mixing, extremely low signal-to-noise ratio, and very large image scales or real-time operation — each of these a separate demonstration context rather than one joint requirement. As of August 2026, the authors' own follow-up has extended the method to real Raman maps of pharmaceutical tablets (online 2022, in print 2023) and adjacent chemometric lines have automated pixel selection or initial estimation for flat, non-hierarchical MCR, but no published work automates the hierarchical decomposition parameters.

Background

Spectral (hyperspectral) imaging records, at every pixel of a sample, a full spectrum — Raman, near-infrared (NIR), infrared, or, in electron microscopy, energy-dispersive X-ray spectroscopy (EDXS) spectra whose peaks mark chemical elements. When the spatial resolution is coarse relative to the scale of phase segregation, most pixels contain mixtures, and the analytical task becomes blind source separation: recover the pure-compound spectra (the spectral signatures) and their spatial abundance maps without reference measurements. Multivariate curve resolution (MCR) addresses this with a bilinear model, X≈AS+EX \approx AS + E, decomposing the pixel-by-wavelength matrix XX into an abundance matrix AA and a signature matrix SS (with residual EE), typically fitted by alternating least squares (MCR-ALS) under physical constraints such as non-negativity and closure (abundances summing to one per pixel). A long-standing difficulty is that the bilinear decomposition is not unique (rotational ambiguity: several pairs (A,S)(A, S) explain the data equally well) and that an unknown number of components, trace species present in only a few pixels, and mixed pixels all degrade the resolution. For count-based data (EDXS, low-signal Raman), the least-squares steps are further corrupted by Poisson noise; the variant MCR-LLM replaces them with Poisson log-likelihood maximization and performs well at low signal-to-noise ratios (SNR). Fauteux-Lefebvre, Lavoie and Gosselin (2018) built on MCR-LLM a hierarchical methodology: the image is recursively split into pixel subgroups so that each subgroup contains fewer coexisting species, making the local bilinear resolution better conditioned; principal component analysis (PCA — a linear projection onto orthogonal directions of maximum variance) of the subgroup spectra guides the decomposition, and the final signatures are picked from the PCA score plot. Demonstrated on simulated EDXS images containing three chemical elements, the method blindly identified and mapped the compounds. Its decisive inputs, however, were chosen by the analyst: the hierarchical stopping criteria (maximum number of levels and minimum pixel size per subgroup), the number of pure components K, and the PCA-score coordinates defining the final spectral signatures. The paper proposed no automated way to set these inputs, their optimal values depend on dataset size, SNR, and chemical complexity, and because the published demonstration was confined to simulated EDXS images of three chemical elements, performance at extremely low SNR, on other spectroscopic modalities, on truly unknown species counts, on nonlinear mixing, and at very large image scales remains untested for it.

Problem Statement

The problem, as posed by the source methodology's open questions, is to make hierarchical MCR a fully operator-independent blind-analysis workflow, in two linked parts serving one overarching objective — removing the analyst dependence and the untested-domain limitation of blind compound identification and mapping in spectral images.

(1) Establish an automated procedure that determines, from the spectral image itself and without per-dataset analyst intervention, the inputs that are currently manual: the hierarchical stopping criteria (maximum number of decomposition levels and minimum pixel size per subgroup), the number of pure components K, and the selection of the final spectral signatures from the PCA score plot — with validity across dataset sizes, SNR regimes, and chemical complexities.

(2) Validate the resulting blind identification and mapping beyond the original demonstration on simulated EDXS data with three chemical elements. The conditions that the published demonstrations have left uncovered — other spectroscopic modalities (e.g., Raman, near-infrared; the authors' 2022/2023 follow-up has already demonstrated the manually configured hierarchy on real Raman tablet maps, so what remains for Raman is a demonstration of the automated parameter determination), samples with a truly unknown number of species, many overlapping peaks, nonlinear mixing effects, extremely low signal-to-noise ratio (where the dwell time, that is the per-pixel spectrum-acquisition time, is short enough that few photons are counted per pixel), 3D data, and very large images or real-time applications — are separate demonstration contexts for this validation rather than a single conjunctive requirement: each is independently informative about the automated workflow, and none is a prerequisite for the others. Since independently established composition is scarce for the hardest of these cases, the validation may rest on whatever evidence suits the sample at hand — simulated data with known composition, reference materials, or orthogonal measurements.

Later literature has already covered part of this terrain — real Raman tablet mapping in 2022, and automated pixel selection, parameter-free initialization and real-time unmixing for flat (non-hierarchical) MCR — so what remains open is the automation of the hierarchical decomposition's own analyst-set inputs, together with demonstration of the automated workflow under the uncovered conditions listed above.

References

  1. Clémence Fauteux-Lefebvre, Francis B. Lavoie, Ryan Gosselin (2018), 'A Hierarchical Multivariate Curve Resolution Methodology To Identify and Map Compounds in Spectral Images', Analytical Chemistry 90(21):13118–13125, DOI 10.1021/acs.analchem.8b04626, https://doi.org/10.1021/acs.analchem.8b04626
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