A comparison of convex and non-convex compressed sensing applied to multidimensional NMR

Kazimierczuk, Krzysztof; Orekhov, Vladislav Yu.

doi:10.1016/j.jmr.2012.08.001

Cited by 50 publications

(43 citation statements)

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“…23 For the l 1 -norm based reconstruction method, we have used Iteractive Soft Thresolding (IST) [23][24][25] but other algorithms, based on different principles, have also been suggested. [26][27][28] In addition to IST, we tried a greedy algorithm (CLEAN) as an example of the latter. 29 In all the examples we tried IST seems to produce better spectra than CLEAN, although CLEAN seems to require less computing time.…”

Section: Resultsmentioning

confidence: 99%

HD-2D: routine high-dispersion two-dimensional NMR spectra at no extra cost

et al. 2016

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(2016) 'HD-2D : routine high-dispersion two-dimensional NMR spectra at no extra cost. ', RSC advances., 6 (86). pp. 83380-83385. Further information on publisher's website:http://dx.doi.org/10.1039/C6RA14471CPublisher's copyright statement:Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractThe synergic use of Pure Shift NMR techniques and Compressive Sensing allows the recording of two-dimensional NMR spectra with much higher dispersion (effective resolution) than can be achieved using conventional techniques. This gain requires no additional hardware and no increase in experiment time. We show that this combination of techniques can be implemented routinely and illustrate the significant advantages that result, enabling analyses that would otherwise have been extremely problematic.

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Section: Resultsmentioning

confidence: 99%

HD-2D: routine high-dispersion two-dimensional NMR spectra at no extra cost

et al. 2016

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“…The figure shows the obtained sum of the CRLBs for the parameters, i.e., tr I(ŵ; θ) −1 , where the sampling pattern is obtained by solving (7) for the case of K = 1 using the model (8), for a singleton set Θ and identity weighting A(θ) = I. This is done for varying values of λ such that the number of samples used vary between M = 5 and M = 25.…”

Section: A Optimization Vs Simulationmentioning

confidence: 99%

“…For high-dimensional data, it quickly becomes infeasible to sample the field uniformly, especially when examining living cells, which have limited lifetimes. This has caused an interest in formulating sampling schemes for NMR signals, allowing for notable improvements [4]- [8]. For example, a recent study of 4-D NMR measurements that would have taken about 2.5 years to perform using regular sampling was shown to be possible to construct in merely 90 hours using a non-uniform sampling scheme [9].…”

Section: Introductionmentioning

confidence: 99%

“…Among the developed schemes are some exploiting a compressive sensing framework, allowing for an accurate signal reconstruction using fewer samples than the Nyquist-Shannon sampling theorem necessitates for uniformly sampled signals (see, e.g., [7], [8]). However, the developed schemes typically do not optimize the sampling scheme with respect to the expected signals, even though these are often fairly well known.…”

Section: Introductionmentioning

confidence: 99%

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Designing optimal sampling schemes

Swärd

Elvander

Jakobsson

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-In this work, we propose a method for finding an optimal, non-uniform, sampling scheme for a general class of signals in which the signal measurements may be non-linear functions of the parameters to be estimated. Formulated as a convex optimization problem reminiscent of the sensor selection problem, the method determines an optimal sampling scheme given a suitable estimation bound on the parameters of interest. The formulation also allows for putting emphasis on a particular set of parameters of interest by scaling the optimization problem in such a way that the bound to be minimized becomes more sensitive to these parameters. For the case of imprecise a priori knowledge of these parameters, we present a framework for customizing the sampling scheme to take such uncertainty into account. Numerical examples illustrate the efficiency of the proposed scheme.

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“…In particular, the two-dimensional (2-D) case has been investigated in several works, such as [3][4][5], wherein the authors examine algorithms based on the problem's eigenvector structure, exploit a sparsity framework, as well as a subspace framework, respectively. Further works include [6], which examined the 3-D case, [7,8], wherein different compressed sensing methods are compared for high dimensional NMR signals, and [8,9], which examined high-dimensional subspace based estimators. Several works also focus on one of the computationally most efficient ways of forming multidimensional sinusoidal paramThis work was supported in part by the Swedish Research Council and the Crafoord's and Carl Trygger's foundations.…”

Section: Introductionmentioning

confidence: 99%

Computationally efficient estimation of multi-dimensional spectral lines

Swärd

Adalbjörnsson

Jakobsson

2016

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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In this work, we propose a computationally efficient algorithm for estimating multi-dimensional spectral lines. The method treats the data tensor's dimensions separately, yielding the corresponding frequency estimates for each dimension. Then, in a second step, the estimates are ordered over dimensions, thus forming the resulting multidimensional parameter estimates. For high dimensional data, the proposed method offers statistically efficient estimates for moderate to high signal to noise ratios, at a computational cost substantially lower than typical non-parametric Fourier-transform based periodogram solutions, as well as to state-of-the-art parametric estimators.

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A comparison of convex and non-convex compressed sensing applied to multidimensional NMR

Cited by 50 publications

References 50 publications

HD-2D: routine high-dispersion two-dimensional NMR spectra at no extra cost

HD-2D: routine high-dispersion two-dimensional NMR spectra at no extra cost

Designing optimal sampling schemes

Computationally efficient estimation of multi-dimensional spectral lines

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