The causality principle in the reconstruction of sparse NMR spectra

Mayzel, Maxim; Kazimierczuk, Krzysztof; Orekhov, Vladislav Yu.

doi:10.1039/c4cc03047h

Cited by 102 publications

(71 citation statements)

References 38 publications

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“…2014). In this way, the number of the unknowns (missing points to be reconstructed) is reduced, and the effectiveness of the procedure is increased.…”

Section: Resultsmentioning

confidence: 99%

Pitfalls in compressed sensing reconstruction and how to avoid them

et al. 2016

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Multidimensional NMR can provide unmatched spectral resolution, which is crucial when dealing with samples of biological macromolecules. The resolution, however, comes at the high price of long experimental time. Non-uniform sampling (NUS) of the evolution time domain allows to suppress this limitation by sampling only a small fraction of the data, but requires sophisticated algorithms to reconstruct omitted data points. A significant group of such algorithms known as compressed sensing (CS) is based on the assumption of sparsity of a reconstructed spectrum. Several papers on the application of CS in multidimensional NMR have been published in the last years, and the developed methods have been implemented in most spectral processing software. However, the publications rarely show the cases when NUS reconstruction does not work perfectly or explain how to solve the problem. On the other hand, every-day users of NUS develop their rules-of-thumb, which help to set up the processing in an optimal way, but often without a deeper insight. In this paper, we discuss several sources of problems faced in CS reconstructions: low sampling level, missassumption of spectral sparsity, wrong stopping criterion and attempts to extrapolate the signal too much. As an appendix, we provide MATLAB codes of several CS algorithms used in NMR. We hope that this work will explain the mechanism of NUS reconstructions and help readers to set up acquisition and processing parameters. Also, we believe that it might be helpful for algorithm developers.Electronic supplementary materialThe online version of this article (doi:10.1007/s10858-016-0068-3) contains supplementary material, which is available to authorized users.

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“…2014). In this way, the number of the unknowns (missing points to be reconstructed) is reduced, and the effectiveness of the procedure is increased.…”

Section: Resultsmentioning

confidence: 99%

Pitfalls in compressed sensing reconstruction and how to avoid them

et al. 2016

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“…In spirit, SMILE is closest to the SSA algorithm (Stanek and Kozminski 2010), but the actual implementation is rather different in terms of peak detection and reconstruction, and takes advantage of the fact that NMR spectra can be phased to become purely absorptive. Taking advantage of this phase information has been used previously to enhance the results of linear prediction algorithms (Zhu and Bax 1990), and for constructing a “virtual echo” which was shown to benefit a range of sparse data reconstruction methods (Mayzel et al 2014). A noteworthy feature of SMILE, which simultaneously benefits spectral resolution and sensitivity, is the automatic extension of the time domain by non-sampled data, which are treated just like the randomly non-sampled data during SMILE reconstruction.…”

Section: Introductionmentioning

confidence: 99%

Sparse multidimensional iterative lineshape-enhanced (SMILE) reconstruction of both non-uniformly sampled and conventional NMR data

et al. 2016

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Implementation of a new algorithm, SMILE, is described for reconstruction of non-uniformly sampled two-, three- and four-dimensional NMR data, which takes advantage of the known phases of the NMR spectrum and the exponential decay of underlying time domain signals. The method is very robust with respect to the chosen sampling protocol and, in its default mode, also extends the truncated time domain signals by a modest amount of non-sampled zeros. SMILE can likewise be used to extend conventional uniformly sampled data, as an effective multidimensional alternative to linear prediction. The program is provided as a plug-in to the widely used NMRPipe software suite, and can be used with default parameters for mainstream application, or with user control over the iterative process to possibly further improve reconstruction quality and to lower the demand on computational resources. For large data sets, the method is robust and demonstrated for sparsities down to ca 1%, and final all-real spectral sizes as large as 300 Gb. Comparison between fully sampled, conventionally processed spectra and randomly selected NUS subsets of this data shows that the reconstruction quality approaches the theoretical limit in terms of peak position fidelity and intensity. SMILE essentially removes the noise-like appearance associated with the point-spread function of signals that are a default of five-fold above the noise level, but impacts the actual thermal noise in the NMR spectra only minimally. Therefore, the appearance and interpretation of SMILE-reconstructed spectra is very similar to that of fully sampled spectra generated by Fourier transformation.

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“…The selected hyper-complex data points were converted to the complex virtual echo representation (Frey et al 2013;Mayzel et al 2014), which contained 174 x 2096 points out of the full complex array with dimensions 174 x 32 x 32…”

Section: Resultsmentioning

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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The causality principle in the reconstruction of sparse NMR spectra

Cited by 102 publications

References 38 publications

Pitfalls in compressed sensing reconstruction and how to avoid them

Pitfalls in compressed sensing reconstruction and how to avoid them

Sparse multidimensional iterative lineshape-enhanced (SMILE) reconstruction of both non-uniformly sampled and conventional NMR data

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

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