Random sampling of evolution time space and Fourier transform processing

Kazimierczuk, Krzysztof; Zawadzka, Anna; Koźmiński, Wiktor; Zhukov, Igor

doi:10.1007/s10858-006-9077-y

Cited by 102 publications

(95 citation statements)

References 37 publications

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“…While this paper was in review, a study by Kazimierczuk et al presenting results for FT processing of randomly distributed sampling points was published [46]. It would be interesting to compare all of these methods in the future.…”

Section: Comparison To Other Sparse Sampling Methodsmentioning

confidence: 98%

Sampling of the NMR time domain along concentric rings

Coggins

Zhou

2007

Journal of Magnetic Resonance

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We present a novel approach to sampling the NMR time domain, whereby the sampling points are aligned on concentric rings, which we term concentric ring sampling (CRS). Radial sampling constitutes a special case of CRS where each ring has the same number of points and the same relative orientation. We derive theoretically that the most efficient CRS approach is to place progressively more points on rings of larger radius, with the number of points growing linearly with the radius, a method that we call linearly increasing CRS (LCRS). For cases of significant undersampling to reduce measurement time, a randomized LCRS (RLCRS) is also described. A theoretical treatment of these approaches is provided, including an assessment of artifacts and sensitivity. The analytical treatment of sensitivity also addresses the sensitivity of radially sampled data processed by Fourier transform. Optimized CRS approaches are found to produce artifact-free spectra of the same resolution as Cartesian sampling, for the same measurement time. Additionally, optimized approaches consistently yield fewer and smaller artifacts than radial sampling, and have a sensitivity equal to Cartesian and better than radial sampling. We demonstrate the method using numerical simulations, as well as a 3-D HNCO experiment on protein G B1 domain.

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Section: Comparison To Other Sparse Sampling Methodsmentioning

confidence: 98%

Sampling of the NMR time domain along concentric rings

Coggins

Zhou

2007

Journal of Magnetic Resonance

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“…It has been shown that the FT of randomly sampled twodimensional time domain signals produces some noise, which is reduced proportionally to the square root of the number of data points. 28 In the conventional and randomly sampled examples shown here the same number of correlation signals was observed. The 'sampling noise' is shown on the traces plotted in Figs 3 and 4.…”

Section: Resultsmentioning

confidence: 73%

“…27 This method was initially applied to radial and spiral sampling, and was later extended to random sampling of the evolution time space. 28 In the case of 3D acquisition, a one-dimensional FID is recorded for each point in the two-dimensional time space with four different modulations in order to fulfill the quadrature requirements. The most important features of the new method are calculation of FT for each pair of frequencies simultaneously and the use of Quaternion notation to describe double quadrature detection.…”

Section: Introductionmentioning

confidence: 99%

Three‐dimensional NMR Spectroscopy of organic molecules by random sampling of evolution time space and multidimensional Fourier transformation

Misiak

Koźmiński

2006

Magnetic Reson in Chemistry

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In this communication we present the application of a new method, which enables one to acquire 3D NMR spectra in a reasonable time and preserves high resolution in indirectly detected domains. The new method is based on random distribution of time domain data points followed by Quaternion FT with respect to two time variables in one step. The experimental examples include three-dimensional spectra of strychnine in CDCl3, TOCSY-HSQC, COSY-HMBC, and the new technique proposed here: heteronuclear single quantum multiple bond correlation (HSQMBC). The obtained spectra are compared to those recorded at the same time employing the conventional acquisition scheme. We show that high-quality 3D spectra of organic compounds can be obtained in reasonable experimental time and that they are of great interest in cases when direct analysis of 2D spectra is difficult.

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“…Recently the two dimensional Fourier transformation (2D-FT) has been re-introduced to transform arbitrarily sampled time domain signals [3][4][5]. In principle the 2D-FT allows the use of non-linear time domain sampling.…”

Section: Introductionmentioning

confidence: 99%

Phasing arbitrarily sampled multidimensional NMR data

Gledhill

Wand

2007

Journal of Magnetic Resonance

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The recent re-introduction of the two dimensional Fourier transformation (2D-FT) has allows for the transformation of arbitrarily sampled time domain signals. In this respect, radial sampling, where two incremented time dimensions (t 1 and t 2 ) are sampled such that t 1 = τ cos α and t 2 = τ sin α, is especially appealing because of the relatively small leakage artifacts that occur upon Fourier transformation. Unfortunately radially sampled time domain data results in a fundamental artifact in the frequency domain manifested as a ridge of intensity extending through the peak positions perpendicular to +/− the radial sampling angle. Successful removal of the ridge artifacts using existing algorithms requires absorptive line shapes. Here we present two procedures for retrospective phase correction of arbitrarily sampled data.

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Random sampling of evolution time space and Fourier transform processing

Cited by 102 publications

References 37 publications

Sampling of the NMR time domain along concentric rings

Sampling of the NMR time domain along concentric rings

Three‐dimensional NMR Spectroscopy of organic molecules by random sampling of evolution time space and multidimensional Fourier transformation

Phasing arbitrarily sampled multidimensional NMR data

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