Applications of Non-Uniform Sampling and Processing

Abstract

Modern high-field NMR instruments provide unprecedented resolution. To make use of the resolving power in multidimensional NMR experiment standard linear sampling through the indirect dimensions to the maximum optimal evolution times (~1.2T ₂) is not practical because it would require extremely long measurement times. Thus, alternative sampling methods have been proposed during the past 20 years. Originally, random nonlinear sampling with an exponentially decreasing sampling density was suggested, and data were transformed with a maximum entropy algorithm (Barna et al., J Magn Reson 73:69–77, 1987). Numerous other procedures have been proposed in the meantime. It has become obvious that the quality of spectra depends crucially on the sampling schedules and the algorithms of data reconstruction. Here we use the forward maximum entropy (FM) reconstruction method to evaluate several alternate sampling schedules. At the current stage, multidimensional NMR spectra that do not have a serious dynamic range problem, such as triple resonance experiments used for sequential assignments, are readily recorded and faithfully reconstructed using non-uniform sampling. Thus, these experiments can all be recorded non-uniformly to utilize the power of modern instruments. On the other hand, for spectra with a large dynamic range, such as 3D and 4D NOESYs, choosing optimal sampling schedules and the best reconstruction method is crucial if one wants to recover very weak peaks. Thus, this chapter is focused on selecting the best sampling schedules and processing methods for high-dynamic range spectra.