A method for joint sparse sampling of time and gradient domains in diffusion-ordered NMR spectroscopy

Nuclear magnetic resonance (NMR) spectroscopy is one of the most valuable tools for chemical analysis. In particular, multidimensional NMR spectra can provide an information on structures of large molecules or complex chemical mixtures. However, because of time-consuming sampling of a multidimensional signal, they require days-long data collection process. This problem has been to some extent circumvented by an application of various sparse sampling techniques in last few years. Nevertheless, they were limited to frequency dimensions of NMR spectra. In this paper, we show how to extend sparse sampling to diffusion dimensions. The procedure is based on a minimum ℓ
₁
-norm restrained Fourier and inverted Laplace transforms. The results of simulations indicate, that the approach can be successfully exploited in experimental studies.