Poisson gap sampling

Hyberts SG, Takeuchi K, Wagner G (2010) Poisson-gap sampling and forward maximum entropy reconstruction for enhancing the resolution and sensitivity of protein NMR data. J Am Chem Soc 132 2145-2147... 

Fig. 5 Woven implementation of NUS Poisson gap sampling schedules in two indirect dimensions. First schedules are created with the selected schedule in the first ti column. This is followed by using the first two rows where the time points have not yet been selected. Subsequently, the next two columns are picked as indicated and so on...

The simulations presented in Fig. 6 show that, with two indirect dimensions, NUS has quite significant benefits in terms of signal to noise and the ability to detect weak peaks. Among the sampling schedules, 5 Exponential and sinusoidal Poisson gap sampling outperform the other sampling schedules. At least seven, and potentially all nine, of the peaks can be observed in the above two cases, while US detects only four or five at best. This is consistent with a previous report that NUS can enhance sensitivity [34]. 

Fig. 7 (continued) dimensions, (c) FM reconstruction of 2,048 (32%) (cl) and 640 (10%) (c2) data points sampled with an exponential weighting schedule in the two indirect dimensions, (d) FM reconstruction of 2,048 (32%) (dl) and 640 (10%) (d2) sampled data points according to weaved sinusoidal Poisson gap sampling. For all spectra, equal numbers of scans were recorded per increment. Thus, the NUS spectra were acquired in one third and one tenth of the time used for the US spectrum, respectively... 

Fig. 8 A menagerie of sampling schemes. The first column depicts examples of two-dimensional sampling schemes that have been employed in NMR, for 30% coverage of a 128 x 128 uniform grid (i.e., approx. 4915 samples out of 16,384). Successive columns depict the PSF for 30%, 10%, and 5% coverage. The PSFs are normalized to the value of the central component, and the color coding is depicted on the far right. Sampling schedules depicted include (c) circular shell, (cr) randomized circular, (r) radial, (Poisson) Poisson gap, (rand) random, (EMS) envelope-matched, (BMS) beat-matched, (burst) bursty, and (triangle) triangular...

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