Non-uniform Sampling (NUS)

Collecting 2D or 3D NMR data can be very time consuming. The indirect dimension of a 2D experiment is sampled linearly via the t1 increments in the pulse sequence.  An FID must be collected for every single linearly spaced t1 increment. In the interest in collecting 2D or 3D NMR data in a more time efficient manner, a great deal of effort is made towards faster data collection techniques.  While some of these methods are based on spatial selectivity, others are based on sparse sampling techniques in the indirect dimensions of nD NMR sequences.  One such sparse sampling method, given the name non-uniform sampling (NUS), samples a sub-set of the indirect dimension in a random (or weighted random) manner and then predicts the uncollected data based on the data sampled, in much the same way data are predicted in the forward and backward linear prediction methods.  The reconstructed data is then used for the indirect Fourier transforms.  A comparison of the conventional and non-uniform data sampling methods is illustrated in the figure below.

Collecting only a fraction of FID's reduces the experiment time by the same fraction.  The figure below shows a superposition of partial 600MHz ¹H-¹³C HSQC spectra of a D₂O solution of sucrose.

All of the spectra were collected with 2 scans per increment using a 1.5 second recycle time.  The lower spectrum in black was collected conventionally with 256 increments in 15 minutes. The middle spectrum in blue was collected conventionally with 64 increments in 3.75 minutes. The top spectrum in purple was collected using NUS with 25% of 256 increments (i.e. 64 increments) collected in 3.75 minutes.  A comparison of the two conventionally collected data sets shows the expected loss in F1 resolution with the 4-fold reduction in experiment time by reducing the number of increments by a factor of 4. The bottom (black) conventional spectrum and the top (purple) NUS spectrum are however virtually indistinguishable despite the 4-fold reduction in experiment time for the NUS spectrum.  NUS is a very valuable technique for reducing experiment times without sacrificing resolution.