Increasing Sensitivity in Determining Chemical Shifts in One Dimensional Lorentzian NMR Spectra

Abstract

An algorithm is presented for one-dimensional NMR systems that employs nonlinear, non-Fourier methods to convert noisy time-dependent free induction decay (FID) data to a denoised frequency spectrum that gives reliable chemical shifts and coupling constants when the spectrum is Lorentzian. It is formulated in a way that increases frequency sensitivity and resolution and, for nuclei of low natural abundance, potentially avoids enrichment totally or in part. The algorithm should also be of use in analytical chemistry where enrichment is not possible. In effect, the useful limit of detection is significantly lowered. The algorithm uses new "phasing" and "feature stability upon accumulation" methods to reliably separate signal from noise at low signal-to-noise ratios where the Fourier spectrum requires many more transients to be definitive as to what is signal and what is noise. The long-standing problem of "false features" that plagued many prior attempts to employ nonlinear methods is thereby resolved for Lorentzian spectra. Examples are reported, and the limitations of the algorithm are discussed.

Dynamic Imaging of Glucose and Lactate Metabolism by 13C-MRS without Hyperpolarization

“…There have been a number of attempts at denoising individual magnetic resonance spectra, either specifically in the context of MRSI or more generally throughout the NMR field. The methods can be divided into those that attempt to denoise the free induction decay (FID) signal in the time domain (Cadzow reduction 38,39 aka HLSVD 39,40 , HTLS 41–43 and Pade transform methods) and those that attempt to directly denoise the MR spectrum in the frequency domain. Time domain methods make the assumption that the signal originates from a small set of ideal Lorentzian peaks with well-defined frequencies, intensities, and line widths 44 .…”

PET by MRI: Glucose Imaging by 13C-MRS without Dynamic Nuclear Polarization by Noise Suppression through Tensor Decomposition Rank Reduction

“…There have been a number of attempts at denoising individual magnetic resonance spectra, either specifically in the context of MRSI or more generally throughout the NMR field. The methods can be divided into those that attempt to denoise the free induction decay (FID) signal in the time domain (Cadzow reduction 41, 42 aka HLSVD 42,43 , HTLS [44][45][46] and Pade transform methods) and those that attempt to directly denoise the MR spectrum in the frequency domain. Time domain methods make the assumption that the signal originates from a small set of ideal Lorentzian peaks with well-defined frequencies, intensities, and line widths.…”

Signal Deconvolution and Noise Factor Analysis Based on a Combination of Time–Frequency Analysis and Probabilistic Sparse Matrix Factorization

“…Conventionally, methods for improving the sensitivity and resolution of FIDs are adjusted by pre-processing steps, such as zero filling and apodization, before Fourier transformation (FT) is carried out [21]. Other methods for reducing mathematical noise from FID signals focus on the region of interest (ROI), such as reference deconvolution [22], harmonic inversion noise removal (HINR) [23], and complete reduction to amplitude frequency table (CRAFT) [24]. In addition, STFT and wavelet transform [25] have been developed as alternative transformation methods to FT for analyzing the relationship between the time and frequency of FIDs.…”

“…It differs from conventional noise reduction using multivariate analysis [34] because it does not require multiple 1D-NMR data that are measured on many samples or acquired with several acquisition parameters. The difference in T 2 * on the time axis determined by performing STFT for each frequency component is useful to separate signals based on MF instead of ROI [22][23][24]. Our method that focuses on the relaxation time utilizes the attenuation behavior of the FID signal without any hardware upgrade for NMR research field.…”