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Criteria for sensitivity enhancement by compressed sensing: practical application to anisotropic NAD 2D-NMR spectroscopy.

Numerous contributions over the last two decades have proven that non-uniform sampling (NUS) allows significant acceleration of NMR experiments. It has been also shown that relaxation-matched NUS can improve the sensitivity when compared to conventional regularly sampled experiments acquired within the same measurement time. The method of compressed sensing (CS), recently introduced to NMR, constitutes an effective approach to NUS processing. However, the relaxation-matched sampling, providing an optimal signal-to-noise ratio, does not optimally fulfill the mathematical criteria of CS reconstruction. In this paper, we show that restricted isometry constants allow prediction of the optimal sampling time constant for exponentially decaying NUS. We also introduce criteria for the choice of the maximal indirect evolution period and we analyze the influence of the maximal indirect evolution period and the sampling time constant on the NUS sensitivity enhancement. As a practical example of application, we have chosen two natural abundance deuterium two dimensional NMR (NAD 2D-NMR) experiments using polypeptide lyotropic chiral liquid crystals (CLCs) as aligning NMR solvents, requiring superior sensitivity and resolution for a wide range of analytical domains (chirality, stereochemistry studies, isotopic fractionation, …). From an experimental viewpoint, the combination of NUS and CS can be successfully applied both for symmetrical anisotropic NAD Q-COSY Fz 2D experiments and asymmetrical NAD Q-resolved Fz ones. The possibility to boost the sensitivity/resolution of anisotropic NAD 2D-NMR experiments opens up new potentialities for the method.