An active constraint approach to identify essential spectral information in noisy data.

Multivariate curve resolution (MCR) methods aim at extracting pure component profiles from mixed spectral data and can be applied to high-dimensional data, e.g., from process spectroscopy or hyperspectral imaging techniques. One often observes that some parts of this data, namely certain rows and columns of the data matrix, are considered essential for MCR outcomes, while other parts are of minor importance. Some methods for determining essential data are known, but all have different disadvantages concerning the application for noisy data. This work presents a new approach on how to detect the essential information for noisy, experimental spectral data. Active nonnegativity constraints in combination with duality arguments are the key ingredients for determining essential spectra and frequency channels. The new approach is conceptually simple, computationally cheap and stable with respect to noise. The algorithm is tested for noisy experimental Raman, UV-Vis and FTIR-SEC data.