Related ArticlesA comparison of convex and non-convex compressed sensing applied to multidimensional NMR.
J Magn Reson. 2012 Oct;223:1-10
Authors: Kazimierczuk K, Orekhov VY
Abstract
The resolution of multidimensional NMR spectra can be severely limited when regular sampling based on the Nyquist-Shannon theorem is used. The theorem binds the sampling rate with a bandwidth of a sampled signal and thus implicitly creates a dependence between the line width and the time of experiment, often making the latter one very long. Recently, Candès et al. (2006) [25] formulated a non-linear sampling theorem that determines the required number of sampling points to be dependent mostly on the number of peaks in a spectrum and only slightly on the number of spectral points. The result was pivotal for rapid development and broad use of signal processing method called compressed sensing. In our previous work, we have introduced compressed sensing to multidimensional NMR and have shown examples of reconstruction of two-dimensional spectra. In the present paper we discuss in detail the accuracy and robustness of two compressed sensing algorithms: convex (iterative soft thresholding) and non-convex (iteratively re-weighted least squares with local l(0)-norm) in application to two- and three-dimensional datasets. We show that the latter method is in many terms more effective, which is in line with recent works on the theory of compressed sensing. We also present the comparison of both approaches with multidimensional decomposition which is one of the established methods for processing of non-linearly sampled data.
Compressed sensing reconstruction of undersampled 3D NOESY spectra: application to large membrane proteins
Compressed sensing reconstruction of undersampled 3D NOESY spectra: application to large membrane proteins
Abstract Central to structural studies of biomolecules are multidimensional experiments. These are lengthy to record due to the requirement to sample the full Nyquist grid. Time savings can be achieved through undersampling the indirectly-detected dimensions combined with non-Fourier Transform (FT) processing, provided the experimental signal-to-noise ratio is sufficient. Alternatively, resolution and signal-to-noise can be improved within a given experiment time. However, non-FT...
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07-30-2012 07:42 AM
Compressed sensing and the reconstruction of ultrafast 2D NMR data: Principles and biomolecular applications.
Compressed sensing and the reconstruction of ultrafast 2D NMR data: Principles and biomolecular applications.
Compressed sensing and the reconstruction of ultrafast 2D NMR data: Principles and biomolecular applications.
J Magn Reson. 2011 Apr;209(2):352-8
Authors: Shrot Y, Frydman L
A topic of active investigation in 2D NMR relates to the minimum number of scans required for acquiring this kind of spectra, particularly when these are dictated by sampling rather than by sensitivity considerations. Reductions in this minimum number of scans have...
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07-23-2011 08:54 AM
[NMR paper] Accuracy and robustness of three-way decomposition applied to NMR data.
Accuracy and robustness of three-way decomposition applied to NMR data.
Related Articles Accuracy and robustness of three-way decomposition applied to NMR data.
J Magn Reson. 2005 Jun;174(2):188-99
Authors: Luan T, Orekhov VY, Gutmanas A, Billeter M
Three-way decomposition is a very versatile analysis tool with applications in a variety of protein NMR fields. It has been used to extract structural data from 3D NOESYs, to determine relaxation rates in large proteins, to identify ligand binding in screening for lead compounds, and to complement...
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11-25-2010 08:21 PM
[Stan NMR blog] A convex functions inequality
A convex functions inequality
An inequality on means of convex function values at points evenly distributed over an interval.
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A comparison of convex and non-convex compressed sensing applied to multidimensional NMR.
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