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

TL;DR

This paper introduces a novel BSS method for 2D HSQC NMR data using ${eta}$-divergence and sparsity regularization, improving the analysis of complex chemical mixtures.

Contribution

It proposes a new variational formulation and optimization strategy specifically tailored for high-dimensional, low-resolution NMR spectral data.

Findings

Effective separation of chemical mixture components demonstrated on simulated data.

Method outperforms traditional approaches in accuracy and computational efficiency.

Validated on real NMR data, showing practical applicability.

Abstract

Nuclear Magnetic Resonance (NMR) spectroscopy is an efficient technique to analyze chemical mixtures in which one acquires spectra of the chemical mixtures along one ore more dimensions. One of the important issues is to efficiently analyze the composition of the mixture, this is a classical Blind Source Separation (BSS) problem. The poor resolution of NMR spectra and their large dimension call for a tailored BSS method. We propose in this paper a new variational formulation for BSS based on a ${\beta}$-divergence data fidelity term combined with sparsity promoting regularization functions. A majorization-minimization strategy is developped to solve the problem and experiments on simulated and real 2D HSQC NMR data illustrate the interest and the effectiveness of the proposed method.