Nuclear magnetic resonance (NMR) spectroscopy serves as an indispensable tool in chemistry and biology but often suffers from long experimental times. We present a proof-of-concept of the application of deep learning and neural networks for high-quality, reliable, and very fast NMR spectra reconstruction from limited experimental data. We show that the neural network training can be achieved using solely synthetic NMR signals, which lifts the prohibiting demand for a large volume of realistic training data usually required for a deep learning approach.

Accelerated Nuclear Magnetic Resonance Spectroscopy with Deep Learning

Nuclear magnetic resonance (NMR) spectroscopy serves as an indispensable tool in chemistry and biology but often suffers from long experimental time. We present a proof-of-concept of application of deep learning and neural network for high-quality, reliable, and very fast NMR spectra reconstruction from limited experimental data. We show that the neural network training can be achieved using solely synthetic NMR signal, which lifts the prohibiting demand for a large volume of realistic training data usually required in the deep learning approach.

Since the concept of deep learning (DL) was formally proposed in 2006, it has had a major impact on academic research and industry. Nowadays, DL provides an unprecedented way to analyze and process data with demonstrated great results in computer vision, medical imaging, natural language processing, and so forth. Herein, applications of DL in NMR spectroscopy are summarized, and a perspective for DL as an entirely new approach that is likely to transform NMR spectroscopy into a much more efficient and powerful technique in chemistry and life sciences is outlined.

Review and Prospect: Deep Learning in Nuclear Magnetic Resonance Spectroscopy.

Spatial encoding and spatial selection methods in high-resolution NMR spectroscopy.

Many signals are modeled as a superposition of exponential functions in spectroscopy of chemistry, biology, and medical imaging. This paper studies the problem of recovering exponential signals from a random subset of samples. We exploit the Vandermonde structure of the Hankel matrix formed by the exponential signal and formulate signal recovery as Hankel matrix completion with Vandermonde factorization (HVaF). A numerical algorithm is developed to solve the proposed model and its sequence convergence is analyzed theoretically. Experiments on synthetic data demonstrate that HVaF succeeds over a wider regime than the state-of-the-art nuclear-norm-minimization-based Hankel matrix completion method, while it has a less restriction on frequency separation than the state-of-the-art atomic norm minimization and fast iterative hard thresholding methods. The effectiveness of HVaF is further validated on biological magnetic resonance spectroscopy data.

Vandermonde Factorization of Hankel Matrix for Complex Exponential Signal Recovery—Application in Fast NMR Spectroscopy

G oal: The two dimensional magnetic resonance spectroscopy (MRS) possesses many important applications in bioengineering but suffers from long acquisition duration. Non-uniform sampling has been applied to the spatiotemporally encoded ultrafast MRS, but results in missing data in the hybrid time and frequency plane. An approach is proposed to recover this missing signal, of which enables high quality spectrum reconstruction. M ethods: The natural exponential characteristic of MRS is exploited to recover the hybrid time and frequency signal. The reconstruction issue is formulated as a low rank enhanced Hankel matrix completion problem and is solved by a fast numerical algorithm. R esults: Experiments on synthetic and real MRS data show that the proposed method provides faithful spectrum reconstruction, and outperforms the state-of-the-art compressed sensing approach on recovering low-intensity spectral peaks and robustness to different sampling patterns. C onclusion: The exponential signal property serves as an useful tool to model the time-domain MRS signals and even allows missing data recovery. The proposed method has been shown to reconstruct high quality MRS spectra from non-uniformly sampled data in the hybrid time and frequency plane. S ignificance: Low-intensity signal reconstruction is generally challenging in biological MRS and we provide a solution to this problem. The proposed method may be extended to recover signals that generally can be modeled as a sum of exponential functions in biomedical engineering applications, e.g., signal enhancement, feature extraction, and fast sampling.

Low Rank Enhanced Matrix Recovery of Hybrid Time and Frequency Data in Fast Magnetic Resonance Spectroscopy

Nuclear magnetic resonance spectroscopy serves as an important tool for analyzing chemicals and biological metabolites. However, its performance is subject to the magnetic-field homogeneity. Under inhomogeneous fields, peaks are broadened to overlap each other, introducing difficulties for assignments. Here, we propose a method termed as line broadening interference (LBI) to provide high-resolution information under inhomogeneous magnetic fields by employing certain gradients in the indirect dimension to interfere the magnetic-field inhomogeneity. The conventional spectral-line broadening is thus interfered to be non-diagonal, avoiding the overlapping among adjacent resonances. Furthermore, an inhomogeneity correction algorithm is developed based on pattern recognition to recover the high-resolution information from LBI spectra. Theoretical deductions are performed to offer systematic and detailed analyses on the proposed method. Moreover, experiments are conducted to prove the feasibility of the proposed method for yielding high-resolution spectra in inhomogeneous magnetic fields.

Line broadening interference for high-resolution nuclear magnetic resonance spectra under inhomogeneous magnetic fields

A method for obtaining high-resolution NMR (nuclear magnetic resonance) spectra in an inhomogeneous magnetic field relates to a NMR spectrum. The method includes the steps: applying a radio frequency pulse to rotate a magnetization vector from an axis X to a plane XY; evolving while applying coherent gradient in a certain direction; applying a reunion pulse after the evolving is over to acquiring magnetic resonance signals; determining applying manner, intensity and direction of the coherent gradient, the method of which is that a half width LW is used to measure the degree of magnetic field inhomogeneity, Nu is taken as the gyromagnetic ratio of a magnetic core, effective test length of a sample is L, and the applying intensity on the gradient is set to be LW/(NuL); increasing and decreasing the intensity of the gradient to obtain corrected magnetic resonance signals; conducting fourier transforming to obtain coherence spectra of the NMR gradient and the inhomogeneous magnetic field; identifying coherent spectrum via the use of pattern recognition algorithms and recording spectral peak distribution map information; correcting the coherent spectrum; cumulatively projecting the corrected spectrum; finally obtaining one-dimensional high-resolution NMR spectra.

Method for obtaining high-resolution NMR (nuclear magnetic resonance) spectra in inhomogeneous magnetic field

Ultrafast multidimensional nuclear magnetic resonance (NMR) technique serves as an important and powerful tool for analyzing chemical and biological systems. Here, we propose an inverse-k-space along with a systematic processing strategy to improve quality of the ultrafast spectrum in terms of lineshape, signal-to-noise ratio, and adaptability to magnetic-field inhomogeneity. Experiments on phantom solutions and a chemical reaction system were performed to validate the effectiveness of inverse-k-space in enhancing the spectral quality of ultrafast technique. On the basis of its versatility, the inverse-k-space will facilitate applications of multidimensional NMR spectra in the rapid characterization of homogeneous chemical systems as well as in the real-time detection of inhomogeneous reaction systems.

Ultrafast multidimensional nuclear magnetic resonance technique: A proof of concept based on inverse-k-space for convenient and efficient performance

Applications of conventional localized nuclear magnetic resonance correlated spectroscopy are restrained by long acquisition times and poor performance under inhomogeneous magnetic fields. Here, a method that combines the spatiotemporal encoding technique with the localization technique and implements the encoding and decoding in unison with suitable asymmetrical gradients is proposed to obtain high-resolution localized correlated spectra under inhomogeneous fields in greatly reduced times. Experiments on phantom solutions prove its insensitivity to linear field inhomogeneities along three orthogonal axes. Moreover, this method is applied to adipose study of marrow tissue with resolution improvements. The proposed method may offer promising perspectives for fast analyses of biological tissues. Copyright © 2014 John Wiley & Sons, Ltd.

Jian Yang

Papers

Low Rank Enhanced Matrix Recovery of Hybrid Time and Frequency Data in Fast Magnetic Resonance Spectroscopy

Line broadening interference for high-resolution nuclear magnetic resonance spectra under inhomogeneous magnetic fields

Method for obtaining high-resolution NMR (nuclear magnetic resonance) spectra in inhomogeneous magnetic field

Ultrafast multidimensional nuclear magnetic resonance technique: A proof of concept based on inverse-k-space for convenient and efficient performance

High-resolution localized spatiotemporal encoding correlated spectra under inhomogeneous magnetic fields via asymmetrical gradient encoding/decoding.