Framework for and evaluation of bursts in random sampling of multidimensional NMR experiments

The grouping of data in bursts, also referred to as clusters, spikes or clumps, is a common phenomenon in stochastic sampling. There have been several reports that suggest that in NMR, the presence of such bursts is beneficial to spectral reconstruction where data are sampled nonuniformly. In this work, we seek to define a mode of sampling that produces bursts of randomly distributed data in a controlled manner. An algorithm is described for achieving this where the burst length and its uniformity is controlled - we refer to this type of sampling mode as clustered sampling. Measures are introduced for assessing the "burstiness" of nonuniformly sampled data in multiple dimensions and properties of the point-spread-function of these schedules are assessed. The clustered sampling method is applied to samples drawn from an exponentially weighted distribution either distributed randomly or pseudo-randomly by use of a jittering algorithm. The results reveal that bursts introduce characteristic sampling artifacts that are shifted to low frequencies (red shifted), with respect to the signal frequency, and that they produce artifact-reduced regions at frequencies related to the burst length. This observation is contrary to that observed for sampling methods that seek to evenly distribute NUS data, such as jittered or Poisson sampling. Extensive evaluation of simulated data with comparable inherent sensitivity, reveals that at high sampling coverage (25% in 1D), the distribution of the data has little impact on common spectral quality measures. Application of the introduced clustered sampling method to an experimental 3D NOESY experiment showed results consistent with that found for the simulated 1D data. However, in the extremes of very sparse sampling, the results suggest that there may be some advantages associated with incorporation of bursts in nonuniform sampling. The tools and theory presented will serve as a starting point to further explore this novel mode of sampling in NMR.