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Nuclear Magnetic Resonance (NMR) spectroscopy is an efficient technique toanalyze chemical mixtures in which one acquires spectra of the chemicalmixtures along one ore more dimensions. One of the important issues is toefficiently analyze the composition of the mixture, this is a classical BlindSource Separation (BSS) problem. The poor resolution of NMR spectra and theirlarge dimension call for a tailored BSS method. We propose in this paper a newvariational formulation for BSS based on a ${\beta}$-divergence data fidelityterm combined with sparsity promoting regularization functions. Amajorization-minimization strategy is developped to solve the problem andexperiments on simulated and real 2D HSQC NMR data illustrate the interest andthe effectiveness of the proposed method.

Unmixing 2D HSQC NMR mixtures with ${\beta}$-NMF and sparsity