Abstract
Modern nuclear magnetic resonance spectroscopy (NMR) is based on two- and higher-dimensional experiments that allow the solving of molecular structures, i.e., determine the relative positions of single atoms very precisely. However, rich chemical information comes at the price of long data acquisition times (up to several days). This problem can be alleviated by compressed sensing (CS)—a method that revolutionized many fields of technology. It is known that CS performs the most efficiently when measured objects feature a high level of compressibility, which in the case of NMR signal means that its frequency domain representation (spectrum) has a low number of significant points. However, many NMR spectroscopists are not aware of the fact that various well-known signal acquisition procedures enhance compressibility and thus should be used prior to CS reconstruction. In this study, we discuss such procedures and show to what extent they are complementary to CS approaches. We believe that the survey will be useful not only for NMR spectroscopists but also to inspire the broader signal processing community.
Highlights
Nuclear Magnetic Resonance spectroscopy (NMR) is currently one of the most versatile techniques of chemical and physical analysis
The free induction decay signal (FID) is induced in a receiver coil of an NMR spectrometer by oscillating effective magnetization of nuclear magnetic moments polarized by an external magnetic field and excited by a radio frequency (RF) pulse
In the language of NMR spectroscopy, k is, roughly speaking, the number of points contributing to peaks
Summary
Nuclear Magnetic Resonance spectroscopy (NMR) is currently one of the most versatile techniques of chemical and physical analysis. Other techniques include the projection spectroscopy based on co-sampling of several indirect time dimensions [22], covariance spectroscopy based on non-Fourier analysis of the conventionally sampled data [23], extrapolation of such data using linear prediction [24] or attempts to remove aliasing from sampling below Nyquist rate [25]. Their effectiveness is based on the compressibility of the spectrum, the relationship to compressed sensing is loose and they are out of scope of this study. We find it beneficial to share lessons from NMR spectroscopy with experts of the broadly defined signal processing field
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