Abstract
Multidimensional nuclear magnetic resonance (NMR) spectroscopy is one of the most crucial detection tools for molecular structure analysis and has been widely used in biomedicine and chemistry. However, the development of NMR spectroscopy is hampered by long data collection time. Non-uniform sampling empowers rapid signal acquisition by collecting a small subset of data. Since the sampling rate is lower than that of the Nyquist sampling ratio, undersampling artifacts arise in reconstructed spectra. To obtain a high-quality spectrum, it is necessary to apply reasonable prior constraints in spectrum reconstruction models. The self-learning subspace method has been shown to possess superior advantages than that of the state-of-the-art low-rank Hankel matrix method when adopting high acceleration in data sampling. However, the self-learning subspace method is time-consuming due to the singular value decomposition in iterations. In this paper, we propose a fast self-learning subspace method to enable fast and high-quality reconstructions. Aided by parallel computing, the experiment results show that the proposed method can reconstruct high-fidelity spectra but spend less than 10% of the time required by the non-parallel self-learning subspace method.
Highlights
Multidimensional nuclear magnetic resonance (NMR) spectroscopy plays an important role in the fields of biomedicine and chemistry [1,2,3]
Since the peak width will not affect the rank, low-rank Hankel matrix (LRHM) offers better reconstructions for these challenging peaks, even though low-intensity peaks, referring to small singular values in the matrix rank minimization, may be compromised or even lost in LRHM reconstructions [22]. This problem exists in general low-rank matrix reconstruction and has been alleviated by introducing the truncated nuclear norm (TNN) to preserve the small singular values in the reconstruction [23]
We found that the subspace of the Hankel matrix corresponds to spectral peaks, and the TNN provides one approach to incorporate the subspace information
Summary
Multidimensional nuclear magnetic resonance (NMR) spectroscopy plays an important role in the fields of biomedicine and chemistry [1,2,3]. The low rank approach transforms the time-domain NMR signal (called free induction decay (FID)) into a Hankel matrix, and explores the low rankness of this matrix. It is called a low-rank Hankel matrix (LRHM) method. Since the peak width will not affect the rank, LRHM offers better reconstructions for these challenging peaks, even though low-intensity peaks, referring to small singular values in the matrix rank minimization, may be compromised or even lost in LRHM reconstructions [22]. NMR data show that compared with the SLS, the fast SLS approach saves considerable time without sacrificing spectrum quality and enables faster reconstruction with parallel computing
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
