| 1. |
- Kazimierczuk, Krzysztof, et al.
(författare)
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Generalized Fourier Transform for Non-Uniform Sampled Data
- 2012
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Ingår i: Novel Sampling Approaches in Higher Dimensional NMR. - Berlin : Springer-Verlag Berlin. - 0340-1022. - 9783642271601 ; 316, s. 79-124
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Bokkapitel (refereegranskat)abstract
- Fourier transform can be effectively used for processing of sparsely sampled multidimensional data sets. It provides the possibility to acquire NMR spectra of ultra-high dimensionality and/or resolution which allow easy resonance assignment and precise determination of spectral parameters, e. g., coupling constants. In this chapter, the development and applications of non-uniform Fourier transform is presented.
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| 2. |
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| 3. |
- Kazimierczuk, Krzysztof, et al.
(författare)
-
A comparison of convex and non-convex compressed sensing applied to multidimensional NMR
- 2012
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Ingår i: Journal of Magnetic Resonance. - : Elsevier BV. - 1090-7807. ; 223, s. 1-10
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Tidskriftsartikel (refereegranskat)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, Candes 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. (C) 2012 Elsevier Inc. All rights reserved.
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| 4. |
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| 5. |
- Kazimierczuk, Krzysztof, et al.
(författare)
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Non-uniform sampling: Post-Fourier era of NMR data collection and processing
- 2015
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Ingår i: Magnetic Resonance in Chemistry. - : Wiley. - 0749-1581 .- 1097-458X. ; 53:11, s. 921-926
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Tidskriftsartikel (refereegranskat)abstract
- The invention of multidimensional techniques in the 1970s revolutionized NMR, making it the general tool of structural analysis of molecules and materials. In the most straightforward approach, the signal sampling in the indirect dimensions of a multidimensional experiment is performed in the same manner as in the direct dimension, i.e. with a grid of equally spaced points. This results in lengthy experiments with a resolution often far from optimum. To circumvent this problem, numerous sparse-sampling techniques have been developed in the last three decades, including two traditionally distinct approaches: the radial sampling and non-uniform sampling. This mini review discusses the sparse signal sampling and reconstruction techniques from the point of view of an underdetermined linear algebra problem that arises when a full, equally spaced set of sampled points is replaced with sparse sampling. Additional assumptions that are introduced to solve the problem, as well as the shape of the undersampled Fourier transform operator (visualized as so-called point spread function), are shown to be the main differences between various sparse-sampling methods. Copyright © 2015 John Wiley & Sons, Ltd.
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| 6. |
- Kazimierczuk, Krzysztof, et al.
(författare)
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Resolution enhancement in NMR spectra by deconvolution with compressed sensing reconstruction
- 2020
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Ingår i: Chemical Communications. - : Royal Society of Chemistry (RSC). - 1359-7345 .- 1364-548X. ; 56, s. 14585-14588
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Tidskriftsartikel (refereegranskat)abstract
- NMR spectroscopy is one of the basic tools for molecular structure elucidation. Unfortunately, the resolution of the spectra is often limited by inter-nuclear couplings. The existing workarounds often alleviate the problem by trading it for another deficiency, such as spectral artefacts or difficult sample preparation and, thus, are rarely used. We suggest an approach using the coupling deconvolution in the framework of compressed sensing (CS) spectra processing that leads to a major increase in resolution, sensitivity, and overall quality of NUS reconstruction. A new mathematical description of the decoupling by deconvolution explains the effects of thermal noise and reveals a relation with the underlying assumption of the CS. The gain in resolution and sensitivity for challenging molecular systems is demonstrated for the key HNCA experiment used for protein backbone assignment applied to two large proteins: intrinsically disordered 441-residue Tau and a 509-residue globular bacteriophytochrome fragment. The approach will be valuable in a multitude of chemistry applications, where NMR experiments are compromised by the homonuclear scalar coupling. This journal is
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| 7. |
- Mayzel, Maxim, et al.
(författare)
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The causality principle in the reconstruction of sparse NMR spectra
- 2014
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Ingår i: Chemical Communications. - : Royal Society of Chemistry (RSC). - 1359-7345. ; 50:64, s. 8947-8950
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Tidskriftsartikel (refereegranskat)abstract
- Non-uniform sampling offers a dramatic increase in the power and efficiency of magnetic resonance techniques in chemistry, molecular structural biology, and other fields. Here we show that use of the causality property of an NMR signal is a general approach for major reduction of measuring time and quality improvement of the sparsely detected spectra.
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| 8. |
- Orekhov, Vladislav, 1966, et al.
(författare)
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Data Processing Methods: Fourier and Beyond
- 2023
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Ingår i: Two-Dimensional (2D) NMR Methods. - 9781119806721 ; , s. 19-46
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Bokkapitel (refereegranskat)abstract
- This chapter presents a compact overview of both practical and rigorously mathematical aspects of modern NMR signal processing. It discusses the properties of the Fourier transform (FT), which will be later useful to explain the effects of the experimental imperfections and signal processing procedures. The fast FT algorithm, used to calculate the discrete FT requires the same number of points in the input and output. However, one can increase the number of spectral points to any desired value by zero filling, that is, extending the free induction decay by adding artificial data points equal to zero at the end. The quadrature detection in one-dimensional spectra is realized through the acquisition of the two modulations, interpreted as real and imaginary parts of a complex NMR signal. The Projection Theorem is a powerful tool, useful in accelerating NMR experiments of dimensionality three and more.
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| 9. |
- Urbanczyk, Mateusz, et al.
(författare)
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Iterative Thresholding Algorithm for Multiexponential Decay Applied to PGSE NMR Data
- 2013
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Ingår i: Analytical Chemistry. - : American Chemical Society (ACS). - 0003-2700 .- 1520-6882. ; 85:3, s. 1828-1833
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Tidskriftsartikel (refereegranskat)abstract
- Pulsed gradient spin echo (PGSE) is a well-known NMR technique for determining diffusion coefficients. Various signal processing techniques have been introduced to solve the task, which is especially challenging when the decay is multiexponential with an unknown number of components. Here, we introduce a new method for the processing of such types of signals. Our approach modifies the Tikhonov’s regularization, known previously in CONTIN and Maximum Entropy (MaxEnt) methods, by using the -norm penalty function. The modification enforces sparsity of the result, which improves resolution, compared to both mentioned methods. We implemented the Iterative Thresholding Algorithm for Multiexponential Decay (ITAMeD), which employs the -norm minimization, using the Fast Iterative Shrinkage Thresholding Algorithm (FISTA). The proposed method is compared with the Levenberg–Marquardt-Fletcher fitting, Non-negative Least Squares (NNLS), CONTIN, and MaxEnt methods on simulated datasets, with regard to noise vulnerability and resolution. Also, the comparison with MaxEnt is presented for the experimental data of polyethylene glycol (PEG) polymer solutions and mixtures of these with various molecular weights (1080 g/mol, 11840 g/mol, 124700 g/mol). The results suggest that ITAMeD may be the method of choice for monodispersed samples with “discrete” distributions of diffusion coefficients.
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| 10. |
- Urbanczyk, M., et al.
(författare)
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Monitoring polydispersity by NMR diffusometry with tailored norm regularisation and moving-frame processing
- 2016
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Ingår i: Analyst. - : Royal Society of Chemistry (RSC). - 0003-2654 .- 1364-5528. ; 141:5, s. 1745-1752
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Tidskriftsartikel (refereegranskat)abstract
- Nuclear magnetic resonance (NMR) is currently one of the main analytical techniques applied in numerous branches of chemistry. Furthermore, NMR has been proven to be useful to follow in situ reactions occurring on a time scale of hours and days. For complicated mixtures, NMR experiments providing diffusion coefficients are particularly advantageous. However, the inverse Laplace transform (ILT) that is used to extract the distribution of diffusion coefficients from an NMR signal is known to be unstable and vulnerable to noise. Numerous regularisation techniques to circumvent this problem have been proposed. In our recent study, we proposed a method based on sparsity-enforcing l(1)-norm minimisation. This approach, which is referred to as ITAMeD, has been successful but limited to samples with a 'discrete' distribution of diffusion coefficients. In this paper, we propose a generalisation of ITAMeD using a tailored l(p)-norm (1 <= p <= 2) to process, in particular, signals arising from 'polydisperse' samples. The performance of our method was tested on simulations and experimental datasets of polyethylene oxides with varying polydispersity indices. Finally, we applied our new method to monitor diffusion coefficient and polydispersity changes of heparin undergoing enzymatic degradation in real time.
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| 11. |
- Wu, Lisha, 1984, et al.
(författare)
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Initial DNA Interactions of the Binuclear Threading Intercalator Λ,Λ-[μ-bidppz(bipy)4Ru2]4+: An NMR Study with [d(CGCGAATTCGCG)]2
- 2013
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Ingår i: Chemistry - A European Journal. - : Wiley. - 0947-6539 .- 1521-3765. ; 19:17, s. 5401-5410
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Tidskriftsartikel (refereegranskat)abstract
- Binuclear polypyridine ruthenium compounds have been shown to slowly intercalate into DNA, following a fast initial binding on the DNA surface. For these compounds, intercalation requires threading of a bulky substituent, containing one RuII, through the DNA base-pair stack, and the accompanying DNA duplex distortions are much more severe than with intercalation of mononuclear compounds. Structural understanding of the process of intercalation may greatly gain from a characterisation of the initial interactions between binuclear RuII compounds and DNA. We report a structural NMR study on the binuclear RuII intercalator -B (-[-bidppz-(bipy)4Ru2]4+; bidppz=11,11’-bis(di-pyrido[3,2-:2’,3’-c]phenazinyl, bipy = 2,2’-bipyridine) mixed with the palindromic DNA [d(CGCGAATTCGCG)]2. Threading of -B depends on the presence and length of AT stretches in the DNA. Therefore, the latter was selected to promote initial binding, but due to the short stretch of AT base pairs, final intercalation is prevented. Structural calculations provide a model for the interaction: -B is trapped in a well-defined surface-bound state consisting of an eccentric minor-groove binding. Most of the interaction enthalpy originates from electrostatic and van der Waals contacts, whereas intermolecular hydrogen bonds may help to define a unique position of -B. Molecular dynamics simulations show that this minor-groove binding mode is stable on a nanosecond scale. To the best of our knowledge, this is the first structural study by NMR spectroscopy on a binuclear Ru compound bound to DNA. In the calculated structure, one of the positively charged Ru2+ moieties is near the central AATT region; this is favourable in view of potential intercalation as observed by optical methods for DNA with longer AT stretches. Circular dichroism (CD) spectroscopy suggests that a similar binding geometry is formed in mixtures of -B with natural calf thymus DNA. The present minor-groove binding mode is proposed to represent the initial surface interactions of binuclear RuII compounds prior to intercalation into AT-rich DNA.
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