Abstract
Reducing the acquisition time for two-dimensional nuclear magnetic resonance (2D NMR) spectra is important. One way to achieve this goal is reducing the acquired data. In this paper, within the framework of compressed sensing, we proposed to undersample the data in the indirect dimension for a type of self-sparse 2D NMR spectra, that is, only a few meaningful spectral peaks occupy partial locations, while the rest of locations have very small or even no peaks. The spectrum is reconstructed by enforcing its sparsity in an identity matrix domain with ℓp (p = 0.5) norm optimization algorithm. Both theoretical analysis and simulation results show that the proposed method can reduce the reconstruction errors compared with the wavelet-based ℓ1 norm optimization.
Highlights
Nuclear magnetic resonance (NMR) spectroscopy is widely utilized to analyze the structures of chemicals and proteins
We will show the advantages of the proposed method in two aspects: (1) identity matrix as the sparsifying transform is compared with wavelet transform; (2) lp norm minimization is compared with l1 norm minimization
The typical l1 norm minimization algorithms compared in this paper include iterative soft thresholding (IST) algorithm [16,41,42,43], alternating and continuation algorithm (ACA) [40]
Summary
Nuclear magnetic resonance (NMR) spectroscopy is widely utilized to analyze the structures of chemicals and proteins. Multidimensional NMR spectra can provide more information than one-dimensional (1D) NMR spectra. The acquisition time for a conventional two-dimensional (2D). NMR spectrum is mostly determined by the number of t1 increments in the indirect dimension. One possible way is to reduce the acquisition time is to reduce the number of t1 increments. This will result in aliasing of the spectrum in the indirect dimension [1,2], because the sampling rate is lower than the requirement of the Nyquist sampling rule. Researchers have been seeking ways to suppress the aliasing from the aspects of sampling and reconstruction. The maximum sampling time for multi-dimensional NMR experiments was analyzed by Vosegaard and co-workers [5]. Some reconstruction algorithms have been employed to improve spectral quality, including maximum entropy [6,7], iterative CLEAN algorithm [8] and Bayesian reconstruction [9]
Sign-in/Register to view highlights & summary 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 callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
