D. van Ormondt

Retrieval of frequencies, amplitudes, damping factors, and phases from time-domain signals using a linear least-squares procedure

Abstract A new method for quantitative analysis of time-domain signals is reported. It amounts to fitting a function consisting of exponentially damped sinusoids with arbitrary phases to the data. By invoking the principle of linear prediction (LP) the fitting can be carried out by a linear least-squares (LS) procedure, and therefore needs no starting values The LS procedure is based on singular value decomposition (SVD), which enables one to distinguish between signal and noise. The method, denoted by LPSVD, yields a list comprising the frequency, damping factor, amplitude, and phase of each retrieved sinusoid. In addition, LPSVD is insensitive to truncation at the beginning and/or the end of the signal, and in fact is capable to accurately reconstruct the missing part. Preprocessing of the data is not necessary. Finally, the method achieves higher resolution than fast Fourier transformation.

SVD-based quantification of magnetic resonance signals

Abstract This study concerns the parametrization of NMR signals by state-space modeling (HSVD), which is based on singular value decomposition. It is shown that nonexponential decay can be parametrized by HSVD (and LPSVD). This property is applied to real-world NMR signals. In addition, we show that under certain conditions the computation time of SVD can be reduced very significantly. This is achieved by using the Lanczos algorithm and exploiting the Hankel structure of the data matrix. Proper orthogonalization of the singular vectors is realized.

Improved algorithm for noniterative time-domain model fitting to exponentially damped magnetic resonance signals

This communication is concerned with a new method of fitting a physical model function to a magnetic resonance signal, directly in the time domain. Our primary aim is analysis of the signal in quantitative terms, i.e., describing the signal in terms of physically meaningful parameters with their statistical errors. Before explaining the new method we make some remarks about the place of time-domain model fitting in spectral analysis. The notion of quantitative description just defined goes beyond constructing a spectrum from the available time-domain data. This judgment is supported by the observation that recently proposed methods for constructing a spectrum (l-3), although very useful for many purposes, have not provided values of the physical parameters involved. In fact, if the latter are wanted afterward, it is then still necessary to fit an appropriate model function to the spectrum (4, 5). Furthermore, in addition to the fitting, the degree to which the spectrum constructed approximates the “ideal” spectrum is to be assessed. On the basis of these considerations, we advocate the use of timedomain model fitting, if quantitative description of a signal is needed. On the other hand, if the primary need is to have a spectrum, one may well use methods such as proposed in Refs. (Z-3), some of which require significantly less computer time. If the signal decays exponentially, which is not uncommon in magnetic resonance, an additional advantage of remaining in the time domain emerges, namely that the fitting procedure can be made noniterative. To the best of our knowledge noniterative fitting procedures are not yet available for the frequency domain. A method of noniterative fitting has recently been devised by Kumaresan and Tufts (6) and was subsequently applied to magnetic resonance (7, 8) under the name LPSVD; see also (9) for a related method. An error analysis was given in (6, IO). We are here concerned with an alternative noniterative model fitting procedure, devised by Kung et al. (II) using the so-called state space formalism. The method can handle considerably more data points than LPSVD because polynomial rooting is avoided. At the same time, the residue of the fit is usually better than that of LPSVD. We shall indicate that the basic idea can be explained with elementary matrix algebra, without invoking the state space formalism. In addition, a formula for efficient computer implementation is given.

Quantitation of magnetic resonance spectroscopy signals: the jMRUI software package

The software package jMRUI with Java-based graphical user interface enables user-friendly time-domain analysis of magnetic resonance spectroscopy (MRS) and spectroscopic imaging (MRSI) and HRMAS-NMR signals. Version 3.x has been distributed in more than 1200 groups or hospitals worldwide. The new version 4.x is a plug-in platform enabling the users to add their own algorithms. Moreover, it offers new functionalities compared to versions 3.x. The quantum-mechanical simulator based on NMR-SCOPE, the quantitation algorithm QUEST and the main MRSI functionalities are described. Quantitation results of signals obtained in vivo from a mouse and a human brain are given.

Time-domain quantitation of 1H short echo-time signals: background accommodation.

Quantitation of 1H short echo-time signals is often hampered by a background signal originating mainly from macromolecules and lipids. While the model function of the metabolite signal is known, that of the macromolecules is only partially known. We present time-domain semi-parametric estimation approaches based on the QUEST quantitation algorithm (QUantitation based on QUantum ESTimation) and encompassing Cramér–Rao bounds that handle the influence of ‘nuisance’ parameters related to the background. Three novel methods for background accommodation are presented. They are based on the fast decay of the background signal in the time domain. After automatic estimation, the background signal can be automatically (1) subtracted from the raw data, (2) included in the basis set as multiple components, or (3) included in the basis set as a single entity. The performances of these methods combined with QUEST are evaluated through extensive Monte Carlo studies. They are compared in terms of bias–variance trade-off. Because error bars on the amplitudes are of paramount importance for diagnostic reliability, Cramér–Rao bounds accounting for the uncertainty caused by the background are proposed. Quantitation with QUEST of in vivo short echo-time 1H human brain with estimation of the background is demonstrated.

Analysis of NMR Data Using Time Domain Fitting Procedures

The beginning of this chapter sets out our main objective and how we intend to achieve it. As the title indicates, the content is concerned with parameter estimation in the time domain. Literally this is correct, but the term Time Domain is to be interpreted as Measurement Domain. Since in-vivo NMR measurements take place in the time domain, these two terms imply the same thing in practice. However, the intended interpretation should be kept in mind.

Resolution enhancement in electron spin-echo spectroscopy by means of the maximum entropy method

Abstract The resolving power of electron spin-echo spectroscopy decreases as the available data segment becomes shorter. A dramatic restoration of the resolving power is achieved by applying maximum entropy spectral analysis. This is possible because the maximum entropy formalism is maximally non-committal with regard to unavailable data.

Quantitation with QUEST of brain HRMAS-NMR signals: Application to metabolic disorders in experimental epileptic seizures

Quantitation of High Resolution Magic Angle Spinning (HRMAS) Nuclear Magnetic Resonance (NMR) signals enables establishing reference metabolite profiles of ex vivo tissues. Signals are often contaminated by a background signal originating mainly from macromolecules and lipids and by residual water which hampers proper quantitation. We show that automatic quantitation of HRMAS signals, even in the presence of a background, can be achieved by the semi‐parametric algorithm QUEST based on prior knowledge of a metabolite basis‐set. The latter was quantum‐mechanically simulated with NMR‐SCOPE and requires accurate spin parameters. The region of interest of spectra is a small part of the full spectral bandwidth. Reducing the computation time inherent to the large number of data‐points is possible by using ER‐Filter in a preprocessing step. Through Monte‐Carlo studies, we analyze the performances of quantitation without and with ER‐Filtering.

Measurement of hyperfine interactions with electron spin-echo spectroscopy. Application to F centers in KCl

Abstract The accuracy of spin-Hamiltonian determination via analysis of electron spin-echo nuclear modulation signals is investigated for F centers in KCl. It turns out that the accuracy matches that of ENDOR. The linewidth of the signals converted to the frequency domain also compares well with ENDOR. Parametric spectrum estimation with autoregressive modeling (maximum entropy method) yields significant further reduction of the linewidth. Analysis of the signal strength in the frequency domain appears feasible.

ESR and ENDOR at 9 and 35 GHz on a powder of the enzyme methanol dehydrogenase from Hyphomicrobium X

ESR and ENDOR at 9 and 35 GHz have been applied to a powder of the enzyme methanol dehydrogenase from Hyphomicrobium X. The observed g‐tensor and ESR linewidth suggest that the protein‐bonded free radical originates from a quinone. ENDOR measurements at 35 GHz show that there are two strongly coupled protons in the free radical. The ENDOR response of the proton with the largest hyperfine coupling has been simulated by means of a line shape model. From this simulation the principal values of the hyperfine tensor could be extracted. The derived values indicate that the proton concerned is attached directly to a carbon of the quinoid ring.