Imaged deconvolution: a method for extracting high-resolution NMR spectra from inhomogeneous fields

We present a novel method for obtaining high resolution NMR spectra in the presence of grossly inhomogeneous magnetic fields, such as those encountered in one-sided access NMR. Our method combines the well-known principle of reference deconvolution with NMR imaging in order to resolve spectral features with frequency resolution orders of magnitude smaller than the prevailing line-broadening due to field inhomogeneity. We demonstrate that, in cases of inhomogeneous field line-broadening more than an order of magnitude larger than the spectral features to be resolved, rather than performing reference deconvolution on the sample as a whole, it is more favourable in terms of SNR to divide the target region of a sample into smaller sub-regions, by means of chemical shift imaging, and then to perform reference deconvolution on the individual sub-region spectra, finally summing the results In this way, significant resolution enhancements can be obtained in the presence of severe magnetic field inhomogeneity without an unacceptable loss in SNR.     

The application of maximum entropy processing to the deconvolution of coupling patterns in NMR

The deconvolution of J-coupling patterns in NMR by iterative maximum entropy processing is demonstrated. Both the in-phase and the antiphase coupling patterns are considered. The deconvolution of the coupling pattern, either for one value of the coupling constant (1D J deconvolution) or for a range of coupling constants (2D J deconvolution) is shown. It is demonstrated that the method can be used for improving the signal-to-noise ratio for known coupling patterns by removing the coupling structure, as well as for extracting coupling constants from an unknown spectrum. Examples are shown both in 1D NMR and in slicewise processing of 2D spectra.     

Spectral restoration using semi-blind deconvolution method with detail-preserving regularization

Peak-details are often smoothed when deconvolution methods are used for spectral restoration. In order to preserve spectral details, detail-preserving regularization is devised and a semi-blind deconvolution method with the detail-preserving regularization (SBD-DP) is proposed. The cost function of SBD-DP is formulated and the numerical solution processes are deduced for restoring spectra and estimating parameter of blur kernel. The deconvolution results of simulated spectra demonstrate that the proposed SBD-DP can restore the spectrum effectively and has a merit on preserving peak details, as well as can estimate the parameter of blur kernel accurately. Then the deconvolution result of experimental Raman spectrum indicates the effectiveness of the proposed SBD-DP method on improving spectral resolution.     

Generalized maximum entropy deconvolution of spectral segments

A maximum entropy Fourier spectral deconvolution (MEFSD) program capable of selecting segments of larger spectra is used to deconvolute overlapping peaks in experimental and synthetic test cases. Low signal-to-noise features in spectra which also have very large features (dynamic ranges 100:1, 1000:1, or more) can be selected for maximum entropy processing by performing calculations on a pseudo-FID constructed from the selected region. Results show efficient and powerful deconvolution with simultaneous noise suppression for spectral segments, even when relatively crowded. Quantitative tests of MEFSD on low signal-to-noise synthetic test spectra, modeled after experimental examples, showed accuracies which were at least as good, or better, in relative peak integrations, over conventional FFT processing followed by Lorentzian curve fitting, for segments from several different test cases with dynamic ranges of 1000:1 to 3:1.     

Extension of deconvolution algorithms for the mapping of moving acoustic sources

Several deconvolution algorithms are commonly used in aeroacoustics to estimate the power level radiated by static sources, for instance, the deconvolution approach for the mapping of acoustic sources (DAMAS), DAMAS2, CLEAN, and the CLEAN based on spatial source coherence algorithm (CLEAN-SC). However, few efficient methodologies are available for moving sources. In this paper, several deconvolution approaches are proposed to estimate the narrow-band spectra of low-Mach number uncorrelated sources. All of them are based on a beamformer output. Due to velocity, the beamformer output is inherently related to the source spectra over the whole frequency range, which makes the deconvolution very complex from a computational point of view. Using the conventional Doppler approximation and for limited time analysis, the problem can be separated into multiple independent problems, each involving a single source frequency, as for static sources. DAMAS, DAMAS2, CLEAN, and CLEAN-SC are then extended to moving sources. These extensions are validated from both synthesized data and real aircraft flyover noise measurements. Comparable performances to those of the corresponding static methodologies are recovered. All these approaches constitute complementary and efficient tools in order to quantify the noise level emitted from moving acoustic sources.     

AssignFit: a program for simultaneous assignment and structure refinement from solid-state NMR spectra

AssignFit is a computer program developed within the XPLOR-NIH package for the assignment of dipolar coupling (DC) and chemical shift anisotropy (CSA) restraints derived from the solid-state NMR spectra of protein samples with uniaxial order. The method is based on minimizing the difference between experimentally observed solid-state NMR spectra and the frequencies back calculated from a structural model. Starting with a structural model and a set of DC and CSA restraints grouped only by amino acid type, as would be obtained by selective isotopic labeling, AssignFit generates all of the possible assignment permutations and calculates the corresponding atomic coordinates oriented in the alignment frame, together with the associated set of NMR frequencies, which are then compared with the experimental data for best fit. Incorporation of AssignFit in a simulated annealing refinement cycle provides an approach for simultaneous assignment and structure refinement (SASR) of proteins from solid-state NMR orientation restraints. The methods are demonstrated with data from two integral membrane proteins, one α-helical and one β-barrel, embedded in phospholipid bilayer membranes.     

Compensation of effect of field instability by reference deconvolution with phase reconstruction

A compensation method based on reference deconvolution is developed to obtain high-resolution NMR spectra under an unstable magnetic field. It is shown that the applicability of the original deconvolution method is limited for small fluctuation, and a process what may be called phase reconstruction is proposed to compensate large field fluctuation. We demonstrate the method using a probe with a coil that can generate a fluctuation field artificially. A high-resolution 1H NMR spectrum of ethylbenzene was obtained under the unstable field after compensation with this method.     

13C CP MAS NMR and GIAO-CHF calculations of coumarins

13C cross-polarization magic-angle spinning NMR spectra were recorded for a series of solid coumarins. Ab initio calculations of shielding constants were performed with the use of GIAO-CHF method. The combined CPMAS NMR and theoretical approach was successful in characterizing solid-state conformations of coumarins; a relationship sigma (ppm) = -1.032 xdelta + 205.28 (R(2) = 0.9845) can be used to obtain structural information for coumarins, for which solid-state NMR or crystal structure data are not available.     

SPINEVOLUTION: a powerful tool for the simulation of solid and liquid state NMR experiments

Exact numerical simulations of NMR experiments are often required for the development of new techniques and for the extraction of structural and dynamic information from the spectra. Simulations of solid-state magic angle spinning (MAS) experiments can be particularly demanding both computationally and in terms of the programming required to carry them out, even if special simulation software is used. We recently developed a number of approaches that dramatically improve the efficiency and allow a high degree of automation of these computations. In the present paper, we describe SPINEVOLUTION, a highly optimized computer program that implements the new methodology. The algorithms used in the program will be described separately. Although particularly efficient for the simulation of experiments with complex pulse sequences and multi-spin systems in solids, SPINEVOLUTION is a versatile and easy to use tool for the simulation and optimization of virtually any NMR experiment. The performance of SPINEVOLUTION was compared with that of another recently developed NMR simulation package, SIMPSON. Benchmarked on a series of examples, SPINEVOLUTION was consistently found to be orders of magnitude faster. At the time of publication, the program is available gratis for non-commercial use.     

Efficient analysis of 51V solid-state MAS NMR spectra using genetic algorithms

A program for iterative fitting procedures to determine the NMR parameters from ⁵¹V solid-state MAS NMR spectra was developed. It contains options to use genetic algorithms and downhill-simplex optimizing procedures to extract the optimal parameter sets, which describe our spectra. As computational kernel the SIMPSON program is employed. Other kernels like SPINEVOLUTION are easily incorporable. The algorithms are checked for their suitability for the present optimization problem and optimal simulation conditions are determined, with the focus on minimal processing time. The procedure leads to a very good agreement between experimental and simulated spectra in a passable period of time. First results for spectra of model compounds for the active site of vanadium haloperoxidases are presented.     

Maximum-entropy deconvolution applied to electron energy-loss spectroscopy

In the present paper, we investigate the performance of maximum-entropy deconvolution, in removing the instrumental response function from electron energy-loss spectra. To this end we make use of spectra acquired from the carbon K-edge in graphite for a range of signal-to-noise ratios. The zero-loss peak is used as the instrumental profile. The resolution improvement obtained through the application of the deconvolution algorithm as a function of the signal-to-noise ratio is well described by a logarithmic dependency. The claimed resolution improvement is further substantiated by demonstrating the consistency between improvement obtained for the width of the instrumental response function, the width of the π¹ peak and the splitting of the σ¹ peaks for a range of signal-to-noise ratios.     

Compact multiframe blind deconvolution

We describe a multiframe blind deconvolution (MFBD) algorithm that uses spectral ratios (the ratio of the Fourier spectra of two data frames) to model the inherent temporal signatures encoded by the observed images. In addition, by focusing on the separation of the object spectrum and system transfer functions only at spatial frequencies where the measured signal is above the noise level, we significantly reduce the number of unknowns to be determined. This "compact" MFBD yields high-quality restorations in a much shorter time than is achieved with MFBD algorithms that do not model the temporal signatures; it may also provide higher-fidelity solutions.     

The application of deconvolution methods in electron spectroscopy — a review

In this review of the application of deconvolution in electron spectroscopy the operations of convolution and deconvolution are first defined. The theoretical background to direct methods, Fourier Transform techniques and iterative approaches to deconvolution is given. The use of smoothing techniques, the removal of secondary electron background and the determination of broadening functions are then considered. Examples of deconvolution in electron spectroscopy are discussed. These include valence and core levels in XPS, gas-phase UPS studies and resolution enhancement in Auger spectroscopy. Deconvolution of Auger spectra to yield density of states curves is examined. The likely future status of deconvolution in electron spectroscopy is considered.     

Iterative deconvolution of X-ray photoelectron spectra generated by an achromatic source

Three cases are presented where X-ray photoelectron spectra generated by an achromatic X-ray source have been deconvoluted by the iterative, Van Cittert method. These are (i the gold 4 f doublet, (ii) the gold valence band, and (iii) the aluminium 2 p spectrum of an oxidized aluminium foil. All prominent features in the deconvolute are shown to be real by comparison with high resolution studies, and the noise levels are low. Resolution after deconvolution is similar to that obtained with a monochromatized X-ray source. The spectra are also similar to those obtained by Fourier transform deconvolution.     

A new deconvolution procedure for ESR spectra

Quantitative determination of spin contents from complex spectra requires deconvolution of each peak. There are several ways to perform this task, the more common being the use of a non-linear fit such as the Marquardt–Levenberg algorithm (M–L). However this technique although very powerful and largely diffused fails when the initial set of parameters of the peaks are far from the true ones, i.e. when the sample composition is not a-priori completely known. In this case a new run with different initial values is required. This isn’t convenient for an automatic deconvolution procedure. Here a new procedure is presented, based on a genetic algorithm as a first step and a M–L method as the second step. The first step will always work regardless of the initial set of data but the accuracy obtainable is lower compared to the M–L technique. The accuracy is improved by using the parameter obtained in a subsequent algorithm employing the M–L method. However, due to the precision of the genetic algorithm presented here, the second step can sometimes be omitted. Results of some trials both on integral and differential spectra are reported and discussed here.     

Spectral semi-blind deconvolution with least trimmed squares regularization

A spectral semi-blind deconvolution with least trimmed squares regularization (SBD-LTS) is proposed to improve spectral resolution. Firstly, the regularization term about the spectrum data is modeled as the form of least trimmed squares, which can help to preserve the peak details better. Then the regularization term about the PSF is modeled as L1-norm to enhance the stability of kernel estimation. The cost function of SBD-LTS is formulated and the numerical solution processes are deduced for deconvolving the spectra and estimating the PSF. The deconvolution results of simulated infrared spectra demonstrate that the proposed SBD-LTS can recover the spectrum effectively and estimate the PSF accurately, as well as has a merit on preserving the details, especially in the case of noise. The deconvolution result of experimental Raman spectrum indicates that SBD-LTS can resolve the spectrum and improve the resolution effectively.     

Application of iterative deconvolution procedures for evaluation of boron depth profiles

The problem of evaluation of boron depth profiles from measured spectra of alpha particles in¹⁰B(n, alpha)⁷Li nuclear reaction is considered. Two iterative deconvolution procedures are examined which may be applied to profile reconstruction. Both techniques have been tested using artificial spectra and they were found to give satisfactory profile reconstruction. The performance of the deconvolution methods is demonstrated by comparison with the measured data.The authors are grateful to their colleagues Dr. J. Vacík and Dr. L. Jahoda for their help in the course of the measurement.     

Spectral deconvolution of NMR cross polarization data sets

The COmponent-REsolved (CORE) strategy has been employed, for the first time to solid state NMR spectroscopy. CORE was used to extract two time-dependent spectral components in 24 ²⁹Si{¹H} NMR spectra, recorded on a meso-structured silica material under conditions of cross polarization evolution. No prior assumptions were made about the component bandshapes, which were both found to be skewed to higher chemical shifts. For the silica fragments close to protons this skewness could be rationalized by a distribution of the degree of condensation in the silica network; however, for the other component the non-Gaussian shape was unexpected. We expect that the same strategy could be applied to a range of experiments in solid-state NMR spectroscopy, where spectral distributions or kinetic parameters need to be accurately extracted.     

A Quantum-Chemical Investigation of the Geometry and NMR Chemical Shifts of Bilirubin

A computational investigation using density-functional-theory methods has been performed concerning the structure and nuclear magnetic resonance (NMR) chemical shifts of bilirubin with a special emphasis on the hydrogen bonds. Solid-state effects on the NMR spectra are investigated by considering a trimeric model derived from the available X-ray structure. Satisfactory agreement between theory and experiment is found with ring-current effects playing only a minor role for the interpretation of the solid-state NMR spectra. Authors' address: Jürgen Gauss, Institut für Physikalische Chemie, Universit?t Mainz, 55099 Mainz, Germany     

Fourier deconvolution of photoacoustic FTIR spectra

Fourier self-deconvolution is a fairly routine numerical method for increasing the apparent resolution of spectra in which the intrinsic bandwidths are much greater than the instrumental resolution. The present work demonstrates that a photoacoustic (PA) interferogram obtained with a Fourier transform spectrometer can be used directly in this calculation, without the usual intermediate computation of a spectrum. Phase errors in the interferogram must be eliminated as a first step in this procedure. The technique has been applied to PA IR interferograms acquired for an Alberta coal and for kaolinite, a common layer silicate. Several new bands were identified in the coal spectrum and assigned utilizing previously published results for coal. Results for kaolinite illustrate a behaviour characteristic of deconvolution of single bands; in addition, an OH-stretching band usually not detectable in IR spectra of kaolinite was observed and verified by comparison with Raman data.