NMR diffusometry and its flagship layout, diffusion-ordered spectroscopy (DOSY), are versatile for studying mixtures of bioorganic and synthetic molecules, but a limiting factor of its applicability is the requirement of a mathematical treatment capable of distinguishing molecules with similar spectra or diffusion constants. We present here a processing strategy for DOSY, a synergy of two high-performance blind source separation (BSS) techniques: non-negative matrix factorization (NMF) using additional sparse conditioning (SC), and the JADE (joint approximate diagonalization of eigenmatrices) declination of independent component analysis (ICA). While the first approach has an intrinsic affinity for NMR data, the latter one can be orders of magnitude computationally faster and can be used to simplify the parametrization of the former.

Fourier transform is the data processing naturally associated to most NMR experiments. Notable exceptions are Pulse Field Gradient and relaxation analysis, the structure of which is only partially suitable for FT. With the revamp of NMR of complex mixtures, fueled by analytical challenges such as metabolomics, alternative and more apt mathematical methods for data processing have been sought, with the aim of decomposing the NMR signal into simpler bits. Blind Source Separation is a very broad definition regrouping several classes of mathematical methods for complex signal decomposition that use no hypothesis on the form of the data. Developed outside NMR , these algorithms have been increasingly tested on spectra of mixtures. In this review, we shall provide an historical overview of the application of Blind Source Separation methodologies to NMR , including methods specifically designed for the specificity of this spectroscopy.