title: Deterministic multidimensional nonuniform gap sampling.
abstract: Born from empirical observations in nonuniformly sampled multidimensional NMR data relating to gaps between sampled points, the Poisson-gap sampling method has enjoyed widespread use in biomolecular NMR. While the majority of nonuniform sampling schemes are fully randomly drawn from probability densities that vary over a Nyquist grid, the Poisson-gap scheme employs constrained random deviates to minimize the gaps between sampled grid points. We describe a deterministic gap sampling method, based on the average behavior of Poisson-gap sampling, which performs comparably to its random counterpart with the additional benefit of completely deterministic behavior. We also introduce a general algorithm for multidimensional nonuniform sampling based on a gap equation, and apply it to yield a deterministic sampling scheme that combines burst-mode sampling features with those of Poisson-gap schemes. Finally, we derive a relationship between stochastic gap equations and the expectation value of their sampling probability densities.
authors.affiliation: Department of Chemistry, University of Nebraska-Lincoln, Lincoln, NE 68588-0304, United States.
authors.forename: Bradley
authors.initials: B
authors.lastname: Worley
authors.affiliation: Department of Chemistry, University of Nebraska-Lincoln, Lincoln, NE 68588-0304, United States. Electronic address: rpowers3@unl.edu.
authors.forename: Robert
authors.initials: R
authors.lastname: Powers
mesh_terms: D000465:Algorithms; D005583:Fourier Analysis; D019906:Nuclear Magnetic Resonance, Biomolecular / Q000379:methods*; D016012:Poisson Distribution; D013269:Stochastic Processes
keywords: Deterministic sampling; NMR; NUS; Poisson-gap