Alexandra Shchukina ;Paweł Kasprzak ;Mateusz Urbańczyk ;Krzysztof Kazimierczuk
Conventional acquisition of two-dimensional (2D) NMR signals is based on an equidistant sampling in both time dimensions. The expected signal bandwidth determines the minimum sampling rate; the desired spectral resolution determines the maximum sampling time. Together, these two principles contribute to a minimum number of sampling points required for satisfactory spectrum quality. Additionally, it takes a few seconds for nuclei to relax between the acquisition of consecutive FID signals in a 2D interferogram. These three requirements cause 2D NMR experiments to last even tens of hours, in extreme cases. One of the standard methods to avoid lengthy data collection is to omit a significant proportion of sampling points during acquisition and reconstruct them later using dedicated algorithms. Such an approach to data acquisition is known as non-uniform sampling (NUS). The reconstruction algorithms exploit specific features of the measured signal, usually some form of compressibility. In this chapter, we will discuss the fundamentals of NUS methods including (a) motivation to use NUS in 2D NMR; (b) basic math behind the reconstruction algorithms; (c) commonly used distributions of sampling points; and (d) the use of related approaches in diffusometry, relaxometry, serial experiments and pure-shift NMR.