NMR signal enhancement via a new time-frequency transform

Time-Frequency Analysis of Two-Dimensional Electron Spin Resonance Signals

Two-dimensional electron spin resonance (2D ESR) spectroscopy is a unique experimental technique for probing protein structure and dynamics, including processes that occur at the microsecond time scale. While it provides significant resolution enhancement over the one-dimensional experimental setup, spectral broadening and noise make extraction of spectral information highly challenging. Traditionally, two-dimensional Fourier transform (2D FT) is applied for the analysis of 2D ESR signals, although its efficiency is limited to stationary signals. In addition, it often fails to resolve overlapping peaks in 2D ESR. In this work, we propose a time-frequency analysis of 2D time-domain signals, which identifies all frequency peaks by decoupling a signal into its distinct constituent components via projection on the time-frequency plane. The method utilizes 2D undecimated discrete wavelet transform (2D UDWT) as an intermediate step in the analysis, followed by signal reconstruction and 2D FT. We have applied the method to a simulated 2D double quantum coherence (DQC) signal for validation and a set of experimental 2D ESR signals, demonstrating its efficiency in resolving overlapping peaks in the frequency domain, while displaying frequency evolution with time in case of non-stationary data.

Sensor Configuration and Algorithms for Power-Line Interference Suppression in Low Field Nuclear Magnetic Resonance

Low field (LF) nuclear magnetic resonance (NMR) shows potential advantages to study pure heteronuclear J-coupling and observe the fine structure of matter. Power-line harmonics interferences and fixed-frequency noise peaks might introduce discrete noise peaks into the LF-NMR spectrum in an open environment or in a conductively shielded room, which might disturb J-coupling spectra of matter recorded at LF. In this paper, we describe a multi-channel sensor configuration of superconducting quantum interference devices, and measure the multiple peaks of the 2,2,2-trifluoroethanol J-coupling spectrum. For the case of low signal to noise ratio (SNR) < 1, we suggest two noise suppression algorithms using discrete wavelet analysis (DWA), combined with either least squares method (LSM) or gradient descent (GD). The de-noising methods are based on spatial correlation of the interferences among the superconducting sensors, and are experimentally demonstrated. The DWA-LSM algorithm shows a significant effect in the noise reduction and recovers SNR > 1 for most of the signal peaks. The DWA-GD algorithm improves the SNR further, but takes more computational time. Depending on whether the accuracy or the speed of the de-noising process is more important in LF-NMR applications, the choice of algorithm should be made.

Denoising of MR spectroscopic imaging data using statistical selection of principal components

OBJECTIVES

To evaluate a new denoising method for MR spectroscopic imaging (MRSI) data based on selection of signal-related principal components (SSPCs) from principal components analysis (PCA).

MATERIALS AND METHODS

A PCA-based method was implemented for selection of signal-related PCs and denoising achieved by reconstructing the original data set utilizing only these PCs. Performance was evaluated using simulated MRSI data and two volumetric in vivo MRSIs of human brain, from a normal subject and a patient with a brain tumor, using variable signal-to-noise ratios (SNRs), metabolite peak areas, Cramer-Rao bounds (CRBs) of fitted metabolite peak areas and metabolite linewidth.

RESULTS

In simulated data, SSPC determined the correct number of signal-related PCs. For in vivo studies, the SSPC denoising resulted in improved SNRs and reduced metabolite quantification uncertainty compared to the original data and two other methods for denoising. The method also performed very well in preserving the spectral linewidth and peak areas. However, this method performs better for regions that have larger numbers of similar spectra.

CONCLUSION

The proposed SSPC denoising improved the SNR and metabolite quantification uncertainty in MRSI, with minimal compromise of the spectral information, and can result in increased accuracy.

New denoising scheme for magnetic resonance spectroscopy signals

A new scheme for denoising magnetic resonance spectroscopy (MRS) signals is presented. This scheme is based on projecting noisy MRS signals in different domains, consecutively, and performing noise filtering operations in these domains. The domains are chosen such that the noise portion, which is inseparable from the desired signal in one domain, is separable in the other. A set of stable, linear, time-frequency (SLTF) transforms with different resolutions was selected for these projections as an example. Scheme evaluation was performed using extensive MRS signals with various noise levels. Compared with one domain denoising, it was observed that the proposed scheme gives superior results that compensate for the excess computational requirements. The proposed scheme supersedes also the wavelet packet denoising schemes.