2016
DOI: 10.1002/anie.201608048
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Absolute Minimal Sampling in High‐Dimensional NMR Spectroscopy

Abstract: Standard three-dimensional Fourier transform (FT) NMR experiments of molecular systems often involve prolonged measurement times due to extensive sampling required along the indirect time domains to obtain adequate spectral resolution. In recent years, a wealth of alternative sampling methods has been proposed to ease this bottleneck. However, due to their algorithmic complexity, for a given sample and experiment it is often hard to determine the minimal sampling requirement, and hence the maximal achievable e… Show more

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Cited by 21 publications
(38 citation statements)
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“…in which each resonance k is defined by three fit parameters, the frequency ω k , volume A k , and transverse relaxation rate R 2, k , that can be obtained by minimizing the sum of the l 2 ‐norms of the residuals of the cosine and sine modulated interferograms, shown below in Equation : trueχ2=trueprefixmin{}∥∥C()t1-Cexp()t1+∥∥S()t1-Sexp()t1 …”
Section: Uniform Versus Non‐uniform Samplingmentioning
confidence: 99%
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“…in which each resonance k is defined by three fit parameters, the frequency ω k , volume A k , and transverse relaxation rate R 2, k , that can be obtained by minimizing the sum of the l 2 ‐norms of the residuals of the cosine and sine modulated interferograms, shown below in Equation : trueχ2=trueprefixmin{}∥∥C()t1-Cexp()t1+∥∥S()t1-Sexp()t1 …”
Section: Uniform Versus Non‐uniform Samplingmentioning
confidence: 99%
“…complex increments along t 1 , thereby defining the absolute minimal sampling (AMS) condition. In many cases, R 2, k can be treated as a constant for all resonances, which further reduces the number of required increments to N 1 ≥M . In practice, it is advisable to collect a few additional t 1 increments in order to have an over‐determined system of equations.…”
Section: Uniform Versus Non‐uniform Samplingmentioning
confidence: 99%
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“…[4] AMS, which is a generalization of SPEED, [5] directly determines spectral parameters, in particular cross-peak positions and their amplitudes, in the time-domain using a non-linear least-squares fitting approach. It differs from CRAFT, [67] which uses complete time-domain data.…”
mentioning
confidence: 99%
“…Next, for each frequency ω 2 , the corresponding trace S exp ( t 1 , ω 2 ) along t 1 , sampled at N 1 different time points, is represented by a superposition of M exponentially damped sinoids: SAMSfalse(t1,ω2false)=k=1MAkexpfalse(iωkt1R2,kt1false)where the coefficients A k correspond to the amplitudes of the complex sinusoids with frequencies ω k and transverse relaxation rates R 2, k . These parameters are determined by a non-linear least squares fit that minimizes [4] χ2=true‖SAMSfalse(t1,ω2false)Sexpfalse(t1,ω2false)true‖2…”
mentioning
confidence: 99%