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.     

Wavelet-based ultra-high compression of multidimensional NMR data sets

The application of a lossy data compression algorithm based on wavelet transform to 2D NMR spectra is presented. We show that this algorithm affords rapid and extreme compression ratios (e.g., 800:1), providing high quality reconstructed 2D spectra. The algorithm was evaluated to ensure that qualitative and quantitative information are retained in the compressed NMR spectra. Whilst the maximum compression ratio that can be achieved depends on the number of signals and on the difference between the most and the least intense peaks (dynamic range), a compression ratio of 80:1 is affordable even for the challenging case of homonuclear 2D experiments of large biomolecules.     

Assigning uncertainties in the inversion of NMR relaxation data

Recovering the relaxation-time density function (or distribution) from NMR decay records requires inverting a Laplace transform based on noisy data, an ill-posed inverse problem. An important objective in the face of the consequent ambiguity in the solutions is to establish what reliable information is contained in the measurements. To this end we describe how upper and lower bounds on linear functionals of the density function, and ratios of linear functionals, can be calculated using optimization theory. Those bounded quantities cover most of those commonly used in the geophysical NMR, such as porosity, T(2) log-mean, and bound fluid volume fraction, and include averages over any finite interval of the density function itself. In the theory presented statistical considerations enter to account for the presence of significant noise in the signal, but not in a prior characterization of density models. Our characterization of the uncertainties is conservative and informative; it will have wide application in geophysical NMR and elsewhere.     

Two-dimensional Fourier transform of arbitrarily sampled NMR data sets

A new procedure for Fourier transform with respect to more than one time variable simultaneously is proposed for NMR data processing. In the case of two-dimensional transform the spectrum is calculated for pairs of frequencies, instead of conventional sequence of one-dimensional transforms. Therefore, it enables one to Fourier transform arbitrarily sampled time domain and thus allows for analysis of high dimensionality spectra acquired in a short time. The proposed method is not limited to radial sampling, it requires only to fulfill the Nyquist theorem considering two or more time domains at the same time. We show the application of new approach to the 3D HNCO spectrum acquired for protein sample with radial and spiral time domain sampling.     

NMR measurement of bitumen at different temperatures

Heavy oil (bitumen) is characterized by its high viscosity and density, which is a major obstacle to both well logging and recovery. Due to the lost information of T2 relaxation time shorter than echo spacing (TE) and interference of water signal, estimation of heavy oil properties from NMR T2 measurements is usually problematic. In this work, a new method has been developed to overcome the echo spacing restriction of NMR spectrometer during the application to heavy oil (bitumen). A FID measurement supplemented the start of CPMG. Constrained by its initial magnetization (M0) estimated from the FID and assuming log normal distribution for bitumen, the corrected T2 relaxation time of bitumen sample can be obtained from the interpretation of CPMG data. This new method successfully overcomes the TE restriction of the NMR spectrometer and is nearly independent on the TE applied in the measurement. This method was applied to the measurement at elevated temperatures (8-90 degrees C). Due to the significant signal-loss within the dead time of FID, the directly extrapolated M0 of bitumen at relatively lower temperatures (<60 degrees C) was found to be underestimated. However, resulting from the remarkably lowered viscosity, the extrapolated M0 of bitumen at over 60 degrees C can be reasonably assumed to be the real value. In this manner, based on the extrapolation at higher temperatures (> or = 60 degrees C), the M0 value of bitumen at lower temperatures (<60 degrees C) can be corrected by Curie's Law. Consequently, some important petrophysical properties of bitumen, such as hydrogen index (HI), fluid content and viscosity were evaluated by using corrected T2.     

Methods and limitations of NMR data inversion for fluid typing

We introduce two NMR inversion methods within the framework of 1D NMR to extract fluid saturations by varying echo spacing and wait time. The first method connects the T2 distribution of each fluid with the overall apparent T2 distribution using a shift matrix. Each fluid's saturation and T2 distribution are extracted by minimizing the difference between the model T2 distributions and measured apparent T2 distributions. The second method relates a model T2 distribution of each fluid with CPMG echo trains using a global evolution matrix that governs the evolution of magnetization under T1, T2 relaxation, and diffusion. These methods will be useful whenever data are not sufficient for 2D NMR inversion. They are also much faster than 2D for fluid typing. We also point out an inherent limitation associated with NMR inversion methods for fluid typing. Whenever there is singularity in the inversion matrix caused by similar behavior of model function for different fluids, most inversion algorithms remove the solution space associated with the singularity and choose a solution vector of the minimum length. This results in equal proportions of different fluids in the final answer. If prior knowledge such as saturation or T2 shape of the oil is available, there are several methods to tailor the solution to our desired outcome. However, if there is no prior knowledge available, such ambiguity always exists irregardless of the inversion schemes.     

Ultra-high resolution 3D NMR spectra from limited-size data sets

The advantage of the filter diagonalization method (FDM) for analysis of triple-resonance NMR experiments is demonstrated by application to a 3D constant time (CT) HNCO experiment. With a 15N-,13C-labeled human ubiquitin sample (1.0 mM), high spectral resolution was obtained at 500 MHz in 25 min with only 6-8 increments in each of the CT dimensions. This data set size is about a factor of 50-100 smaller than typically required, yet FDM analysis results in a fully resolved spectrum with a sharp peak for each HNCO resonance. Unlike Fourier transform (FT) processing, in which spectral resolution in each dimension is inversely proportional to the acquisition time in this dimension, FDM is a true multi-dimensional method; the resolution in all dimensions is determined by the total information content of the entire signal. As the CT dimensions of the 3D HNCO signal have approximate time-reversal symmetry, they can each be doubled by combining the usual four hyper-complex data sets. This apparent quadrupling of the data is important to the success of the method. Thus, whenever raw sensitivity is not limiting, well-resolved n-dimensional spectra can now be obtained in a small fraction of the usual time. Alternatively, to maximize sensitivity, evolution periods of faster relaxing nuclei may be radically shortened, the total required resolution being obtained through chemical shift encoding of other, more slowly relaxing, spins. Improvements similar to those illustrated with a 3D HNCO spectrum are expected for other triple-resonance spectra, where CT evolution in the indirect dimensions is implemented.     

Uniform-penalty inversion of multiexponential decay data. II. Data spacing, T(2) data, systemic data errors, and diagnostics

The basic method of UPEN (uniform penalty inversion of multiexponential decay data) is given in an earlier publication (Borgia et al., J. Magn. Reson. 132, 65-77 (1998)), which also discusses the effects of noise, constraints, and smoothing on the resolution or apparent resolution of features of a computed distribution of relaxation times. UPEN applies negative feedback to a regularization penalty, allowing stronger smoothing for a broad feature than for a sharp line. This avoids unnecessarily broadening the sharp line and/or breaking the wide peak or tail into several peaks that the relaxation data do not demand to be separate. The experimental and artificial data presented earlier were T(1) data, and all had fixed data spacings, uniform in log-time. However, for T(2) data, usually spaced uniformly in linear time, or for data spaced in any manner, we have found that the data spacing does not enter explicitly into the computation. The present work shows the extension of UPEN to T(2) data, including the averaging of data in windows and the use of the corresponding weighting factors in the computation. Measures are implemented to control portions of computed distributions extending beyond the data range. The input smoothing parameters in UPEN are normally fixed, rather than data dependent. A major problem arises, especially at high signal-to-noise ratios, when UPEN is applied to data sets with systematic errors due to instrumental nonidealities or adjustment problems. For instance, a relaxation curve for a wide line can be narrowed by an artificial downward bending of the relaxation curve. Diagnostic parameters are generated to help identify data problems, and the diagnostics are applied in several examples, with particular attention to the meaningful resolution of two closely spaced peaks in a distribution of relaxation times. Where feasible, processing with UPEN in nearly real time should help identify data problems while further instrument adjustments can still be made. The need for the nonnegative constraint is greatly reduced in UPEN, and preliminary processing without this constraint helps identify data sets for which application of the nonnegative constraint is too expensive in terms of error of fit for the data set to represent sums of decaying positive exponentials plus random noise.     

核磁共振弛豫时间测量数据处理方法的讨论

分析和讨论了在超小型核磁共振成像仪测量弛豫时间T1的数据处理方法中存在的问题,并提出了测量方法和数据拟合的改进方案.     

The coupled dynamics of two particles with different limit sets

We consider a system of two coupled particles evolving in a periodic and spatially symmetric potential under the influence of external driving and damping. The particles are driven individually in such a way that in the uncoupled regime, one particle evolves on a chaotic attractor, while the other evolves on regular periodic attractors. Notably, only the latter supports coherent particle transport. The influence of the coupling between the particles is explored, and in particular how it relates to the emergence of a directed current. We show that increasing the (weak) coupling strength subdues the current in a process, which in phase-space, is related to a merging crisis of attractors forming one large chaotic attractor in phase-space. Further, we demonstrate that complete current suppression coincides with a chaos-hyperchaos transition.     

Correction of errors caused by imperfect inversion pulses in MR imaging measurement of T1 relaxation times

Spin-lattice (T₁) relaxation times were measured by an inversion-recovery magnetic resonance imaging method with a slice-selective inversion pulse (SIP), a non-selective rectangular inversion pulse (RIP), or a B₁-insensitive adiabatic inversion pulse (AIP). Data analysis either assumed perfect inversion (two-parameter fit) or allowed for imperfect inversion (three-parameter fit). Imperfect inversion pulses caused low T₁ values in phantoms with a two-parameter fit, while three-parameter T₁ estimates were accurate over the range 430–2670 ms. A difference of ∼10% between two-parameter and three-parameter T₁ values in normal human brain tissue was attributed to B₁ inhomogeneity with the slice-selective inversion pulse and rectangular inversion pulse, to the slice profile with the slice-selective inversion pulse, and to T₂ effects for the adiabatic inversion pulse. Any T₁ method that relies on accurate flip angles may have a significant systematic error in vivo. Phantom accuracy does not ensure accuracy in vivo, because phantoms may have a more homogeneous B₁ field and a longer T₂ than do biological samples.     

The practical assessment of errors in sound intensity measurement

Many sources of error in two transducer sound intensity measurements have been discussed in the literature. Many of these errors are difficult to assess in a practical situation, but two in particular can be calculated. These are the error associated with phase mis-match and random error. The use of the known phase mis-match is discussed as regards its use in evaluating the quality of a particular measurement, and the use of coherence is discussed as regards its use in calculating random error.     

Fluorescent optical tomography with large data sets

In recent years, optical tomography (OT) of highly scattering biological samples has increasingly relied on noncontact CCD-based imaging devices that can record extremely large data sets, with up to 10(9) independent measurements per sample. Reconstruction of such data sets requires fast algorithms. The latter have been developed and applied experimentally in our previous work to imaging of the intrinsic absorption coefficient of highly scattering media. However, it is widely recognized that the use of fluorescent contrast agents in OT has the potential to significantly enhance the technique. We show that the algorithms previously developed by us can be modified to reconstruct the concentration of fluorescent contrast agents.     

A simple Abel inversion method of interferometric data for temperature measurement in axisymmetric medium

In this work, we describe a simple method of Abel inversion for temperature measurement in a natural convection axisymmetric flow. The essence of the method is that the measured lateral fringe shift profile is fitted with a polynomial with only even powers and then Abel inverse integral is evaluated analytically. This technique is compared with recent existing methods to test the accuracy and error propagation using a simulated interferogram of natural convection flow below a downward-facing heated horizontal disk in air. For this comparison, lateral fringe profiles are simulated using temperature fields computed by solving Navier Stokes and energy equations. Through random-number generation, noise profile is artificially added to the simulated noise-free lateral fringe shift profile. The results showed that the proposed technique for Abel inversion leads to accurate temperature profiles when the lateral fringe shift profile is fitted with even-power polynomials having degrees ranging from 20 to 30.     

反演与拟合相结合处理核磁共振弛豫数据的方法

讨论非负最小二乘（NNLS）法和非线性拟合在分析处理核磁共振（NMR）弛豫数据中的应用.同时将二者结合，提出用NNLS的反演结果来设定非线性拟合初值的方法，并用计算机模拟和实验证明了该方法在分析处理NMR弛豫数据中的有效性. 关键词： 非负最小二乘法 非线性拟合 核磁共振 弛豫时间     

Matching of light fluxes in the analysis of measurement data with different space resolutions

We investigate the effect of the dimensions of instantaneous visual fields and the time of accumulation of a signal on the magnitude of light fluxes, recorded by means of charge-coupled device (CCD)-receivers, in scanning different kinds of surfaces. We show that, to compare light fluxes, it is necessary to introduce weight coefficients that take into account the time during which an area measured with a high space resolution is in the visual field of instrumentation with a low space resolution. Errors in the determination of light fluxes, when data obtained with a high space resolution are summed up with equal weight coefficients, have been evaluated. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 1, pp. 123–126, January–February, 2000.     

Position and momentum densities. Complementarity at work: refining a quantum model from different data sets

Although Bragg and Compton scattering are well-established techniques, only very few attempts to simultaneously combine information originating from these two experiments have been made so far. This remark also holds for Bragg neutron magnetic combined with X-ray scattering. We propose a quite general procedure to refine a quantum model from different data sets using basic Bayesian probability theory. As an illustration, a qualitative preliminary study to extract chemical information such as charge transfer in ionic-covalent compounds is reported.     

Fourier inversion of LEED data

Low-energy electron diffraction intensity profiles are Fourier inverted. The optical transform is more suitable for LEED than the usual cosine transform and yields a quantity related to the autocorrelation function. Transforms of individual LEED profiles taken at different diffraction geometry are not the same, but transforms of averaged, kinematic data give expected autocorrelation functions.