Extraction of multiple pure component 1H and 13C NMR spectra from two mixtures: novel solution obtained by sparse component analysis-based blind decomposition

Sparse Component Analysis (SCA) is proposed for the blind extraction of pure component spectra from measured mixed spectra in 13C and 1H nuclear magnetic resonance (NMR) spectroscopy using two mixtures only. As opposed to independent component analysis (ICA) -based solutions that require the number of linearly independent mixtures to be greater or equal to the number of pure components, the proposed SCA-based approach to deal with the blind source separation (BSS) problem is insensitive to statistical (in)dependence among pure components. The algorithm is formulated exploiting sparseness of the pure components in the wavelet basis defined by either Morlet or Mexican hat wavelet. It is assumed that in average only one pure component exists at each coordinate in the wavelet domain. In contrast to the majority of the BSS algorithms no a priori information about the number of pure components is required because it is estimated during the clustering phase of the algorithm. The method is demonstrated on both 1H and 13C NMR experimental data of a mixture with the known pure component spectra