Compressed Sampling in NMR Spectroscopy

Abstract The introduction of the Fourier transform (FT) half a century ago, as well as a slightly younger concept of multidimensional spectroscopy, revolutionized NMR experiments improving their sensitivity, resolution, and the amount of information provided. However, classical processing of multidimensional NMR data acquired with Nyquist sampling grid requires lengthy measurements and rarely approaches ‘natural’ (relaxation-determined) resolution limits. Since the 1980s, several methods of nonuniform sampling have been proposed to reduce the measurement times by exploiting the sparsity (compressibility) of spectra. The comprehensive theory of the sparsity-based approach, known as compressed sensing or compressive sampling (CS), was formulated around a decade ago and later exploited in NMR, further improving nonuniform sampling (NUS) processing. Nowadays, all NMR software packages include CS as a standard approach to acquire and process NUS NMR data. Here, we summarize the efforts to make CS a reliable NMR technique and discuss its optimizations, variants, and nonstandard applications.