Post-acquisition solvent suppression by singular-value decomposition

Applications of the Whittaker smoother in NMR spectroscopy

The Whittaker smoother, a special case of penalized least square, is a multipurpose algorithm that has proven to be very useful in many scientific fields, including image processing, chromatography, and optical spectroscopy. It shares many similarities with the Savitzky-Golay algorithm, but it is significantly faster and easier to automate. Its use in nuclear magnetic resonance, however, is not widespread although several applications have recently been published. In this review, the mathematical background of the method and its main applications in nuclear magnetic resonance spectroscopy will be discussed.

Pitfalls in compressed sensing reconstruction and how to avoid them

Multidimensional NMR can provide unmatched spectral resolution, which is crucial when dealing with samples of biological macromolecules. The resolution, however, comes at the high price of long experimental time. Non-uniform sampling (NUS) of the evolution time domain allows to suppress this limitation by sampling only a small fraction of the data, but requires sophisticated algorithms to reconstruct omitted data points. A significant group of such algorithms known as compressed sensing (CS) is based on the assumption of sparsity of a reconstructed spectrum. Several papers on the application of CS in multidimensional NMR have been published in the last years, and the developed methods have been implemented in most spectral processing software. However, the publications rarely show the cases when NUS reconstruction does not work perfectly or explain how to solve the problem. On the other hand, every-day users of NUS develop their rules-of-thumb, which help to set up the processing in an optimal way, but often without a deeper insight. In this paper, we discuss several sources of problems faced in CS reconstructions: low sampling level, missassumption of spectral sparsity, wrong stopping criterion and attempts to extrapolate the signal too much. As an appendix, we provide MATLAB codes of several CS algorithms used in NMR. We hope that this work will explain the mechanism of NUS reconstructions and help readers to set up acquisition and processing parameters. Also, we believe that it might be helpful for algorithm developers.

Proton MRS and MRSI of the brain without water suppression

Water suppression (WS) techniques have played a vital role in the commencement and development of in vivo proton magnetic resonance spectroscopy (MRS, including spectroscopic imaging - MRSI). WS not only made in vivo proton MRS functionally available but also made its applications conveniently accessible, and it has become an indispensable tool in most of the routine applications of in vivo proton MR spectroscopy. On the other hand, WS brought forth some challenges. Therefore, various techniques of proton MRS without WS have been developed since the pioneering work in the late 1990s. After more than one and a half decades of advances in both hardware and software, non-water-suppressed proton MRS is coming to the stage of maturity and seeing increasing application in biomedical research and clinical diagnosis. In this article, we will review progress in the technical development and applications of proton MRS without WS.

Denoising NMR time-domain signal by singular-value decomposition accelerated by graphics processing units

We present a post-processing method that decreases the NMR spectrum noise without line shape distortion. As a result the signal-to-noise (S/N) ratio of a spectrum increases. This method is called Cadzow enhancement procedure that is based on the singular-value decomposition of time-domain signal. We also provide software whose execution duration is a few seconds for typical data when it is executed in modern graphic-processing unit. We tested this procedure not only on low sensitive nucleus (29)Si in hybrid materials but also on low gyromagnetic ratio, quadrupole nucleus (87)Sr in reference sample Sr(NO3)2. Improving the spectrum S/N ratio facilitates the determination of T/Q ratio of hybrid materials. It is also applicable to simulated spectrum, resulting shorter simulation duration for powder averaging. An estimation of the number of singular values needed for denoising is also provided.

Automated solvent artifact removal and base plane correction of multidimensional NMR protein spectra by AUREMOL-SSA

Strong solvent signals lead to a disappearance of weak protein signals close to the solvent resonance frequency and to base plane variations all over the spectrum. AUREMOL-SSA provides an automated approach for solvent artifact removal from multidimensional NMR protein spectra. Its core algorithm is based on singular spectrum analysis (SSA) in the time domain and is combined with an automated base plane correction in the frequency domain. The performance of the method has been tested on synthetic and experimental spectra including two-dimensional NOESY and TOCSY spectra and a three-dimensional (1)H,(13)C-HCCH-TOCSY spectrum. It can also be applied to frequency domain spectra since an optional inverse Fourier transformation is included in the algorithm.

Efficient removal of unwanted signals in NMR spectra using the filter diagonalization method

It is often desirable to selectively remove corrupting or uninteresting signals from complex NMR spectra without disturbing overlapping or nearby signals. For biofluids in particular, removal of solvent and urea signals is important for retaining quantitative accuracy in NMR-based metabonomics. This article presents a novel algorithm for efficient filtering of unwanted signals using the filter diagonalization method (FDM). Unwanted signals are modeled in the time domain using FDM. This modeled signal is subtracted from the original free induction decay. The resulting corrected signal is then processed using established workflow. The algorithm is found to be reliable and fast. By eliminating large, broad, uninteresting signals, many spectra can be subjected to fully automated absolute value processing, allowing objective preparation of spectra for pattern recognition analysis.

High dynamic-range magnetic resonance spectroscopy (MRS) time-domain signal analysis

In the absence of water signal suppression, the proton magnetic resonance spectroscopy ((1)H MRS) in vivo water resonance signal-to-noise ratio (SNR) is orders of magnitude larger than the SNR of all the other resonances. In this case, because the high-SNR water resonance dominates the data, it is difficult to obtain reliable parameter estimates for the low SNR resonances. Herein, a new model is described that offers a solution to this problem. In this model, the time-domain signal for the low SNR resonances is represented as the conventional sum of exponentially decaying complex sinusoids. However, the time-domain signal for the high SNR water resonance is assumed to be a complex sinusoid whose amplitude is slowly varying from pure exponential decay and whose phase is slowly varying from a constant frequency. Thus, the water resonance has only an instantaneous amplitude and frequency. The water signal is neither filtered nor subtracted from the data. Instead, Bayesian probability theory is used to simultaneously estimate the frequencies, decay-rate constants, and amplitudes for all the low SNR resonances, along with the water resonance's time-dependent amplitude and phase. While computationally intensive, this approach models all of the resonances, including the water and the metabolites of interest, to within the noise level.

Decimative subspace-based parameter estimation methods of magnetic resonance spectroscopy based on prior knowledge

The method Hankel Total Least Squares (HTLS)-PK, which successfully incorporates prior knowledge of known signal poles into the method HTLS, has been proven to greatly improve the performance for parameter estimation of overlapping peaks of magnetic resonance spectroscopy (MRS) signal. In addition, decimation is also proposed as a way to increase the performance of subspace-based parameter estimation methods in the case of oversampling. Taking advantage of decimation in combination with prior knowledge to estimate the MRS signal parameters, two novel subspace-based parameter estimation methods, HTLSDSumPK and HTLSDStackPK, are presented in this paper. The experimental results and relevant analysis show that the methods HTLSDSumPK, HTLSDStackPK and HTLS-PK are slightly better than the method HTLS at low noise levels; however, the three prior-knowledge-incorporating methods, especially the method HTLSDSumPK, have much better performance than the method HTLS at high noise levels in the terms of robustness, estimated accuracy and computational complexity. Even if some inaccuracy of prior knowledge is considered, the method HTLSDSumPK also shows some advantages.

Residual water suppression by indirect covariance NMR

Residual water solvent signals in 2D NMR experiments adversely affect appearance and subsequent analysis of spectra. A method for water suppression that is based on indirect covariance processing is described. It produces a symmetric spectrum with a water signal that is substantially decreased or completely absent. The method, which can be combined with other water suppression schemes, is demonstrated for 2D TOCSY, NOESY, and ROESY spectra of the protein, ubiquitin in aqueous solution.

WAVEWAT-improved solvent suppression in NMR spectra employing wavelet transforms

WAVEWAT is a new processing algorithm to suppress the on-resonance water signal in NMR spectra. It is based on a multiresolution analysis (MRA) of the free induction decay (FID) using a dyadic discrete wavelet transform (DWT). The width of the suppressed signal can be adjusted so that signals close to water are recovered without distortion of the signal shape and intensity. Computational efficiency is comparable to that of convolution filters employing a Fourier transform.

MR spectroscopy quantitation: a review of time-domain methods

In this article an overview of time-domain quantitation methods is given. Advantages of processing the data in the measurement domain are discussed. The basic underlying principles of the methods are outlined and from them the situations under which these algorithms perform well are derived. Also an overview of methods to preprocess the data is given. In that respect, signal-to-noise and/or resolution enhancement, the removal of unwanted components and corrections for model imperfections are discussed.

Water modeled signal removal and data quantification in localized MR spectroscopy using a time-scale postacquistion method

We have previously shown the continuous wavelet transform (CWT), a signal-processing tool, which is based upon an iterative algorithm using a lorentzian signal model, to be useful as a postacquisition water suppression technique. To further exploit this tool we show its usefulness in accurately quantifying the signal metabolites after water removal. However, due to the static field inhomogeneities, eddy currents, and "radiation damping," the water signal and the metabolites may no longer have a lorentzian lineshape. Therefore, another signal model must be used. As the CWT is a flexible method, we have developed a new algorithm using a gaussian model and found that it fits the signal components, especially the water resonance, better than the lorentzian model in most cases. A new framework, which uses the two models, is proposed. The framework iteratively extracts each resonance, starting by the water peak, from the raw signal and adjusts its envelope to both the lorentzian and the gaussian models. The model giving the best fit is selected. As a consequence, the small signals originating from metabolites when selecting, removing, and quantifying the dominant water resonance from the raw time domain signal are preserved and an accurate estimation of their concentrations is obtained. This is demonstrated by analyzing (1H) magnetic resonance spectroscopy unsuppressed water data collected from a phantom with known concentrations at two different field strengths and data collected from normal volunteers using two different localization methods.

Proton MR spectroscopic imaging without water suppression

To improve reproducibility in proton magnetic resonance (MR) spectroscopic imaging in human brain, simultaneous acquisition of the internal water reference and metabolite signals was evaluated. Measurements in healthy volunteers showed that the increase in dynamic range from signal oversampling was sufficient to avoid digitization errors. In addition, use of singular value decomposition techniques and finite impulse response filters proved effective in separating water and metabolite signals and providing estimates of the metabolite concentrations.

Water peak suppression: time-frequency vs time-scale approach

Wavelets are the most popular time-scale analysis tool. A well-known application of wavelets in nuclear magnetic resonance spectroscopy is water peak extraction/suppression. However, spectroscopists are more familiar with frequency than scale. So, from a spectroscopist point of view, a time-scale analysis tool (i.e., wavelets) is not natural and a time-frequency approach would be much more satisfactory. We explain a time-frequency solution to this problem based on Gabor analysis. As the two formalisms are closely linked together we continuously emphasize their similarities and differences. In particular we show that, here, the Gabor method is as efficient as the wavelet approach, and we give some examples. Those remarks also apply to other NMR problems solved previously with the continuous wavelet transform, such as quantification or dynamical phase correction.

Accurate quantification of (1)H spectra: from finite impulse response filter design for solvent suppression to parameter estimation

A scheme for accurate quantification of (1)H spectra is presented. The method uses maximum-phase finite impulse response (FIR) filters for solvent suppression and an iterative nonlinear least-squares (NLLS) algorithm for parameter estimation. The estimation algorithm takes the filter influence on the metabolites of interest into account and can thereby correctly incorporate a large variety of prior knowledge into the estimation phase. The FIR filter is designed in such a way that no distortion of the important initial samples is introduced. The FIR filter method is compared numerically with the HSVD method for water signal removal in a number of examples. The results show that the FIR method, using an automatic filter design scheme, slightly outperforms the HSVD method in most cases. The good performance and ease of use of the FIR filter method combined with its low computational complexity motivate the use of the proposed method.

Fast Removal of Residual Water in Proton Spectra

Quantification of metabolites in 1H spectra is difficult because of the presence of an unwanted water signal. Preprocessing, or removing the water contribution of a 1H spectrum, in the time domain is usually done using the state-space approach HSVD. HSVD removes the residual water and its side lobes, thereby reducing the baseline for the metabolites of interest and allowing subsequent data analysis using more sophisticated nonlinear least squares algorithms. However, the HSVD algorithm is computationally expensive because it estimates the signal subspace using the singular value decomposition (SVD). We show here that replacing the SVD by a low-rank revealing decomposition speeds up the computations without affecting the accuracy of the wanted parameter estimates. Copyright 1998 Academic Press.