UC Riverside

Nuclear Magnetic Resonance is the premier analytical tool for characterizing chemical structure and dynamics. Yet, it battles with the challenge of relatively low sensitivity. To combat this issue, various schemes have been devised over the years. One such strategy, Non-Uniform Sampling (NUS) refers to any method of collecting variable numbers of transients or irregularly spaced data points in the indirect dimension for signal acquisition in magnetic resonance. Non-Uniform Weighted Sampling (NUWS) is a specific embodiment of NUS that collects non-uniform numbers of repeated measurements on the uniformly sampled Nyquist grid, with the promise of increased sensitivity while retaining the ability to generate the frequency domain spectrum via Fourier transformation. However, there is no consensus on the best way to combine multiple samples at indirect time points. This objective of this study is to showcase the increased sensitivity of weighted non-uniform sampling.

Theoretical and experimental observations shows that the maximum signal-to-noise ratio for NUWS is found when the signal is constructed using consistent RMS noise (UCR) for the time domain signal. An alternate metric to signal-to-noise ratio, called Spectral Knowledge is used to quantify the spectral parameters, which is obtained using Monte Carlo Simulations and Fisher Information estimates. The experimental implementation of NUWS-UCR is demonstrated and the sensitivity gains of NUS are quantified. Another technique BFT-UCR is introduced which can work for acquisition that doesn’t cleave on to the uniform grid yet shows similar sensitivity gains to NUWS-UCR under the densely sampled regime. Multiple weighted and non-weighted sampling strategies have been employed to study the sensitivity advantages and trade-offs associated with weighted NUS, with focus being primarily on the variants of exponentially biased sampling schedules in the dense regime in indirect dimensions.

Both analytic theory and experiment suggest a re-examination of the NUS sensitivity theorem when comparing spectra acquired in the same overall experiment time. Ultimately, both SNR and spectral knowledge point to the efficacy of NUWS, with sensitivity increases of >50% for each indirect dimension under standard acquisition parameters.

It is posited that NUWS-UCR provides the ultimate threshold for sensitivity gains that can be attained under weighted NUS.