Software Package for Non-Uniform Sampling

D. Levi Craft^*, David Rovnyak^*, Adam Schuyler^

* Bucknell University, Department of Chemistry, Lewisburg PA 17837

^ University of Connecticut Health Center, Biophysics Department of Molecular Biology and Biophysics, Farmington CT 06030

Non-uniform sampling (NUS) often means acquiring time domain samples non-consecutively following a sampling density. Robust spectral estimation techniques have been developed to produce high fidelity frequency spectra from NUS NMR data, where it is appropriate to view the samples as constraints on line shapes. Exponential weighted sampling paired with maximum entropy reconstruction (MaxEnt) has been shown through extensive empirical work to yield frequency spectra highly comparable to those that would be obtained by FFT of uniform data.

Line shapes obtained by NUS-MaxEnt may experience a very weak, but non-negligible broadening only near the peak base when employing exponential weighting matched to the signal decay (figure below). However, this problem can be resolved by sinusoidal weighting of an exponential signal, which has the same intrinsic sensitivity as matched exponential NUS, but uses more samples in the regime 0.5-2.0 T2, and does not suffer broadening of peak bases (Figure 1).

Motivated by this finding, we set out to further improve alternatives to exponential densities. For example, a sampling density based on a quadratic function has slightly higher intrinsic SNR than sinusoidal and matched exponential NUS, while still preserving the shapes of peak bases (Figure 1).

Exponential NUS can be biased to even shorter times in order to obtain intrinsic SNR enhancements over two-fold compared to uniform sampling,1ab but the extra SNR comes at a cost. The line width at half height is not perturbed by matched exponential NUS, but is broadened if the NUS is biased further.1b,2 We show that much of the broadening incurred by biased exponential NUS can be mitigated by using alternative densities, such as a squared sinusoidal function that has nearly the same intrinsic SNR, but acquires more samples after 0.5T2 to better constrain the line shape (Figure 2).

Finally, we recently developed a simple algorithm for producing properly gapped, sinusoidally weighted NUS schedules that retain randomness.2 For this work, we extended the algorithm to more sampling densities, and also implemented a new set of deterministic statistical NUS schedules. We will show that MaxEnt-NUS spectra obtained from either the deterministic or the gapped-randomly-weighted schedules were essentially indistinguishable, validating both approaches and giving experimentalists a larger choice of robust NUS schedules.

I will contribute a set of computer programs to a larger software platform hosted at the University of Connecticut Health Center. The aim of my work is to improve the accessibility and effectiveness of an emerging technology known as non-uniform sampling (NUS) for nuclear magnetic resonance (NMR) data collection. My work will help to automate the use of NUS by non-expert users and help to facilitate the sharing and communication of data acquired by NUS.

By implementing sophisticated schedule generators and schedule metrics in programs that are accessible to non-expert users, I hope to develop clear and helpful demonstrations of the benefits of using NUS in NMR data acquisition.

1. (a) Magn. Reson. Chem. V49, 483-491, 2011. (b) J. Phys. Chem. B 116(25): 7416-7427 (2012).

1. J. Biomol. NMR, V58: 303-314, 2014.â?¨