Two-dimensional Fourier transform of arbitrarily sampled NMR data sets

Kazimierczuk, Krzysztof; Koźmiński, Wiktor; Zhukov, Igor

doi:10.1016/j.jmr.2006.02.001

Cited by 136 publications

(115 citation statements)

References 27 publications

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“…One can derive analytically that such a spectrum will reproduce peak positions and shapes correctly, but with corruption of the baseline by a high-order Bessel function in cases of limited sampling. Such an artifact pattern has also been demonstrated empirically by Kazimierczuk and coworkers in a parallel effort, using the generic point-by-point equation for the discrete FT on the radially sampled data [30], although it is important to note that a proper weighting factor is required for each point to produce quantitative spectra [28].…”

Section: Introductionmentioning

confidence: 58%

“…Obtaining a spectrum from CRS data requires an initial processing step before the FT to convert from hypercomplex to complex data, as described previously [6,7,9,28,30]; we recommend that the reader consult [28] for a complete discussion. Briefly, linear combinations are taken of the hypercomplex FIDs to yield complex-valued data.…”

Section: Data Processingmentioning

confidence: 99%

“…Alternatively, one could employ the traditional 2-D point-by-point discrete FT, as recently suggested by Kazimierczuk and colleagues [30], adding a weighting factor as we previously noted [28]: [8] where the summation is over all of the available sampling points, each point j having a position (x j , y j ) and a weight ΔA j that is determined by the distribution of the sampling points. For CRS, this transform would be computed as:…”

Section: Data Processingmentioning

confidence: 99%

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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: Introductionmentioning

confidence: 58%

Section: Data Processingmentioning

confidence: 99%

Section: Data Processingmentioning

confidence: 99%

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Sampling of the NMR time domain along concentric rings

Coggins

Zhou

2007

Journal of Magnetic Resonance

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“…Once the phase corrections are determined the data is retransformed with the appropriate corrections applied to Eq. [9].…”

Section: Theorymentioning

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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“…However, due to the intrinsic problems of choosing the right model and convergence, the parametric algorithms cannot guaranty the detection of all significant signals in a large spectrum. Another approach Multidimensional Fourier Transform (MFT) (Kazimierczuk et al 2006) for large spectra exploits prior knowledge about the signal positions in some or all of the spectral dimensions. MFT reconstructs only small regions around known spectral peaks and thus requires less computations and storage.…”

Section: Introductionmentioning

confidence: 99%

Fast multi-dimensional NMR acquisition and processing using the sparse FFT

et al. 2015

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Increasing the dimensionality of NMR experiments strongly enhances the spectral resolution and provides invaluable direct information about atomic interactions. However, the price tag is high: long measurement times and heavy requirements on the computation power and data storage. We introduce Sparse Fast Fourier Transform (SFFT) as a new method of NMR signal collection and processing, which is capable of reconstructing high quality spectra of large size and dimensionality with short measurement times, faster computations than the Fast Fourier Transform, and minimal storage for processing and handling of sparse spectra. The new algorithm is described and demonstrated for a 4D BEST-HNCOCA spectrum.

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Two-dimensional Fourier transform of arbitrarily sampled NMR data sets

Cited by 136 publications

References 27 publications

Sampling of the NMR time domain along concentric rings

Sampling of the NMR time domain along concentric rings

Phasing arbitrarily sampled multidimensional NMR data

Fast multi-dimensional NMR acquisition and processing using the sparse FFT

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