Interpolating and extrapolating with hmsIST: seeking a tmax for optimal sensitivity, resolution and frequency accuracy

Non-Uniform Sampling has the potential to exploit the optimal resolution of high-field NMR instruments. This is not possible in 3D and 4D NMR experiments when using traditional uniform sampling due to the long overall measurement time. Nominally, uniformly sampled time domain data acquired to a maximum evolution time t(max) can be extended to high resolution via a virtual maximum evolution time t*(max) while extrapolating with linear prediction or iterative soft thresholding (IST). At the high resolution obtainable with extrapolation of US data, however, the accuracy of peak positions is compromised as observed when comparing inter- and intra-residue peaks in a 3D HNCA experiment. However, the accuracy of peak positions is largely improved by spreading the same number of acquired time domain data points non-uniformly over a larger evolution time to an optimal t(max) followed by extrapolation to a total t*(max) and processing the data with an appropriate reconstruction method, such as hmsIST. To explore the optimum value of experimentally measured t(max) to be reached non-uniformly with a given number of sampling points we have created test situations of time-equivalent experiments and evaluate sensitivity and accuracy of peak positions. Here we use signal-to-maximum-noise ratio as the decisive measure of sensitivity. We find that both sensitivity and resolution are optimal when PoissonGap sampling to a t(max) of about A 1/2 *T-2*. Digital resolution is further enhanced by extrapolating the range of acquired time domain data to 2*T-2* but without measuring experimental points beyond A 1/2 *T-2 *.