Evaluating metrics of spectral quality in nonuniform sampling

Abstract

In pursuit of an adaptive approach to nonuniform sampling (NUS), two critical determinants arise: (1) the ability to determine an endpoint by way of quantitatively assessing spectral quality and (2) the ability to systematically determine what additional FIDs to collect if the aforementioned stop criteria is not met. As previously established, in situ receiver operator characteristic (IROC, (Zambrello et al., 2017)) assesses the recovery of injected synthetic ground truth signals to define spectral quality. The Nonuniform Sampling Contest (NUScon, (Pustovalova et al., 2021)), defines a workflow for processing NUS experiments and quantitatively evaluating spectral quality. We augmented that workflow by including an IROC module, which we believe to be an effective component of defining stop criteria for adaptive FID collection. As for the decision of what additional FIDs, this study builds off the work of prior studies on the influence the seed used to generate a nonuniform sample schedule has on the quality of a NUS reconstruction (Hyberts et al., 2011), i.e., whether a sampling method yields “high-variance” or “low-variance” schedules (Zambrello et al., 2020). Namely, existing work has been focused on reducing seed-dependence (Eddy et al., 2012; Mobli, 2015; Worley, 2016) or “optimizing” the seed (Hyberts and Wagner, 2022) by evaluating sample schedules using a computationally inexpensive metric based on the characterization of the point-spread function, like sidelobe-to-peak ratio (Lustig et al., 2007) and peak-to-sidelobe ratio (PSR, (Eddy et al., 2012; Mobli, 2015; Worley, 2016; Craft et al., 2018)). This study assesses the ability of PSR, an a priori metric that is based solely on the nonuniform sample schedule, to predict spectral quality as assessed by IROC. This work uses IROC to show that seed optimization via PSR does not result in better quality spectra. In addition, the trends observed in the spectral quality reported by IROC informs our future designs for adaptive FID selection.