High fidelity sampling schedules for NMR spectra of high dynamic range

The ability to reconstruct non-uniformly sampled (NUS) NMR spectra has mostly been accepted. Still a concern is lingering regarding artifacts from sampling non-uniformly. As experienced, some sampling schedules yield better results than others. Finding a useful schedule is relatively trivial for a low dynamic range spectrum and a conservative sparsity, but not so when the dynamic range is large and/or when extreme sparsity is used. High dynamic range is typically found in NOESY and spectra of metabolites, where quantification of peak heights is desired at high fidelity. Extreme sparsity is desired when high throughput is a goal. In all cases, selecting a poor sampling schedule can create unnecessary artifacts. Effectively, it is important to select a sampling schedule that provides a signal-to-artifact apex ratio (SAAR) value in par or better than the signal-to-noise ratio (SNR) value. Notably, by signal-to-artifact apex ratio we consider reconstruction fidelity as the apex intensity likeness, i.e., as the true signal to the tallest artifact. We show that the quality of reconstruction depends on the particular sampling schedule. We evaluate the reconstruction quality in the frequency domain following a matched Lorentz-to-Gauss transform plus common apodization and Fourier Transform. As the Lorentz-to-Gauss transform improves resolution and reduces ridges we include this when defining the Signal-to-Artifact Apex Ratio (SAAR) metric. This metric measures the ratio of simulated reconstructed peak height to the tallest artifact of reconstruction in a spectrum without noise. Once a NUS schedule is found with an optimal SAAR it will be satisfactory for all spectra recorded with the same parameter set. Tables with good seed values are provided in the supplement.