An esprit-based parameter estimator for spectroscopic data (original) (raw)
Related papers
2001
The problem of estimating the frequencies, dampings, amplitudes and phases of closely spaced complex damped exponentials in the presence of noise is considered. In several papers, decimation is proposed as a way to increase the performance of subspace-based parameter estimation methods, in the case of oversampling. In this paper, a novel extension of the HTLS-method (Hankel-Total Least Squares) that operates directly on the decimated data matrix is presented, and it is compared to other decimation methods. Experiments on simulated nuclear magnetic resonance (NMR) spectroscopy signals show the influence of decimation on the accuracy and computational complexity of the estimators.
Nonlinear-least-squares analysis of slow motional regime EPR spectra
Journal of Magnetic Resonance, 2006
A comparison between the full Newton-type optimization NL2SNO, the Levenberg-Marquardt method with the model-trust region modification, and the simplex algorithm is made in the context of the iterative fitting of EPR spectra. EPR lineshape simulations are based on the stochastic Liouville equation (SLE), with an anisotropic diffusion tensor and an anisotropic restraining potential describing the motional amplitude of the spin label. The simplex algorithm was found to be the most reliable, and an approach-incorporating both NL2SNO as well as the downhill simplex methods-is proposed as a strategy-of-choice.
Journal of Magnetic Resonance, Series A, 1996
The application of the ''model trust region'' modification of the instrumentation. Two of the most important advances in-Levenberg-Marquardt minimization algorithm to the analysis of clude the introduction of two-dimensional Fourier-transform one-dimensional CW EPR and multidimensional Fourier-transmethods (1-4), and the extension of both continuous-wave form (FT) EPR spectra especially in the slow-motion regime is (5, 6, 7) and pulsed (8, 9) EPR methods to high frequencies described. The dynamic parameters describing the slow motion requiring superconducting magnets. By analogy with similar are obtained from least-squares fitting of model calculations based developments in NMR, these enhancements have greatly on the stochastic Liouville equation (SLE) to experimental spectra. increased the amount of structural and dynamic information The trust-region approach is inherently more efficient than the that is available from spectra of spin labels and intrinsic standard Levenberg-Marquardt algorithm, and the efficiency of paramagnetic species. the procedure may be further increased by a separation-of-vari-One important application of EPR, and magnetic resoables method in which a subset of fitting parameters is independently minimized at each iteration, thus reducing the number of nance in general, is to study the molecular dynamics of an parameters to be fitted by nonlinear least squares. A particularly appropriate label in isotropic fluids, ordered phases such useful application of this method occurs in the fitting of multicomas liquid crystals or biological membranes, on surfaces, or ponent spectra, for which it is possible to obtain the relative popuattached to macromolecules. Many details of the dynamics lation of each component by the separation-of-variables method. are discernible in the slow-motion regime (10), where the These advantages, combined with recent improvements in the characteristic time scale of the motion is on the order of the computational methods used to solve the SLE, have led to an inverse spectral bandwidth. However, the analysis of sloworder-of-magnitude reduction in computing time, and have made motion spectra is complicated by the fact that the relationship it possible to carry out interactive, real-time fitting on a laboratory between the spectrum and the physical parameters of interest workstation with a graphical interface. Examples of fits to experiis rather indirect. The partial averaging of EPR spectra by mental data will be given, including multicomponent CW EPR molecular motion or spin dynamics can produce very comspectra as well as two-and three-dimensional FT EPR spectra. Emphasis is placed on the analytic information available from the plicated and irregular lineshapes requiring detailed spectral partial derivatives utilized in the algorithm, and how it may be simulation to extract the desired information. used to estimate the condition and uniqueness of the fit, as well The increase in the number of spectral dimensions and as to estimate confidence limits for the parameters in certain cases. the resolution now available in EPR has been accompanied
ROBUST FREQUENCY-SELECTIVE KNOWLEDGE-BASED PARAMETER ESTIMATION FOR NMR SPECTROSCOPY
ABSTRACT In many magnetic resonance spectroscopy (MRS) applications, one strives to estimate the parameters describing the signal to allow for more precise knowledge of the analyte. Typically, MRS signals are well modelled as a sum of damped sinusoids that has properties that are partly known a priori. FREEK, a recently proposed subspace-based parameter estimation method allows for inclusion of such prior knowledge.
Exploiting Spin Echo Decay in the Detection of Nuclear Quadrupole Resonance Signals
IEEE Transactions on Geoscience and Remote Sensing, 2007
Nuclear quadrupole resonance (NQR) is a radiofrequency technique that can be used to detect the presence of quadrupolar nuclei, such as the 14 N nucleus prevalent in many explosives and narcotics. In a typical application, one observes trains of decaying NQR echoes, in which the decay is governed by the spin echo decay time(s) of the resonant line(s). In most detection algorithms, these echoes are simply summed to produce a single echo with a higher signal-to-noise ratio, ignoring the decaying echo structure of the signal. In this paper, after reviewing current NQR signal models, we propose a novel NQR data model of the full echo train and detail why and how these echo trains are produced. Furthermore, we refine two recently proposed approximative maximum-likelihood detectors that enable the algorithms to optimally exploit the proposed echo train model. Extensive numerical evaluations based on both simulated and measured NQR data indicate that the proposed detectors offer a significant improvement as compared to current state-of-the-art detectors.
The Journal of Physical Chemistry A, 2019
This paper is a continuation of the method introduced by Srivastava and Freed (2017) that is a new method based on truncated singular value decomposition (TSVD) for obtaining physical results from experimental signals without any need for Tikhonov regularization or other similar methods that require a regularization parameter. We show here how to estimate the uncertainty in the SVD-generated solutions. The uncertainty in the solution may be obtained by finding the minimum and maximum values over which the solution remains converged. These are obtained from the optimum range of singular value contributions, where the width of this region depends on the solution point location (e.g., distance) and the signal-to-noise ratio (SNR) of the signal. The uncertainty levels typically found are very small with substantial SNR of the (denoised) signal, emphasizing the reliability of the method. With poorer SNR, the method is still satisfactory but with greater uncertainty, as expected. Pulsed dipolar electron spin resonance spectroscopy experiments are used as an example, but this TSVD approach is general and thus applicable to any similar experimental method wherein singular matrix inversion is needed to obtain the physically relevant result. We show that the Srivastava–Freed TSVD method along with the estimate of uncertainty can be effectively applied to pulsed dipolar electron spin resonance signals with SNR > 30, and even for a weak signal (e.g., SNR ≈ 3) reliable results are obtained by this method, provided the signal is first denoised using wavelet transforms (WavPDS).
Improved modeling and bounds for NQR spectroscopy signals
2014
Nuclear Quadrupole Resonance (NQR) is a method of detection and unique characterization of compounds containing quadrupolar nuclei, commonly found in many forms of explosives, narcotics, and medicines. Typically, multi-pulse sequences are used to acquire the NQR signal, allowing the resulting signal to be well modeled as a sum of exponentially damped sinusoidal echoes. In this paper, we improve upon the earlier used NQR signal model, introducing an observed amplitude modulation of the spectral lines as a function of the sample temperature. This dependency noticeably affects the achievable identification performance in the typical case when the substance temperature is not perfectly known. We further extend the recently presented Cramér-Rao lower bound to the more detailed model, allowing one to determine suitable experimental conditions to optimize the detection and identifiability of the resulting signal. The theoretical results are carefully motivated using extensive NQR measurements.
2010
One of the major challenges is using subspace-based approaches for the determination of the parameters of one-or multidimensional signals is their practical applicability on real data containing damped exponentials. In this paper, we present a comparison survey of low complexity subspacebased methods and we focus on 2-D nuclear magnetic resonance (NMR) spectroscopy application. We first present free search 2-D estimation approaches for damped sinusoids and we analyze their performances using simulated signals. Then, we present the results obtained on real 2-D NMR data.
Localised high resolution spectral estimator for resolving superimposed peaks in NMR signals
Signal Processing
Nuclear magnetic resonance (NMR) spectroscopy is the prime technique for studying molecular and biomolecular structure as well as dynamics. The time domain NMR signal can be ideally modelled as the sum of damped complex exponentials in additive Gaussian noise. The spectrum of the signal may contain regions having overlapping peaks. In order to understand the underlying chemical structure, these peaks need to be detected and resolved. In this paper, we propose the Localised Capon Estimator (LoCapE) for resolving closely spaced peaks in the NMR spectrum when the actual number of peaks is unknown. The novel method is able to efficiently retrieve the correct number of components and obtain high resolution spectral estimates in the selected regions of the spectrum. LoCapE is tested with simulated and actual proton NMR spectra to verify its performance.
Compressive Spectral Estimation with Single-Snapshot ESPRIT: Stability and Resolution
ArXiv, 2016
In this paper Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) is developed for spectral estimation with single-snapshot measurement. Stability and resolution analysis with performance guarantee for Single-Snapshot ESPRIT (SS-ESPRIT) is the main focus. In the noise-free case, exact reconstruction is guaranteed for any arbitrary set of frequencies as long as the number of measurement data is at least twice the number of distinct frequencies to be recovered. In the presence of noise and under the assumption that the true frequencies are separated by at least two times Rayleigh's Resolution Length, an explicit error bound for frequency reconstruction is given in terms of the dynamic range and the separation of the frequencies. The separation and sparsity constraint compares favorably with those of the leading approaches to compressed sensing in the continuum.