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Reconstruction of Self-Sparse 2D NMR Spectra from Undersampled Data in the Indirect Dimension†
Department of Communication Engineering, Fujian Key Laboratory of Plasma and Magnetic Resonance, Xiamen University, Xiamen 361005, China
Department of Electronic Science, Fujian Key Laboratory of Plasma and Magnetic Resonance, Xiamen 361005, China
School of Software, Shanghai Jiao Tong University, Shanghai 200240, China
† A one page abstract of this work was presented at the 18th Scientific Meeting of the International Society for Magnetic Resonance in Medicine, Stockholm, Sweden, 1–7 May 2010; p. 3371.
* Author to whom correspondence should be addressed.
Received: 31 July 2011; in revised form: 31 August 2011 / Accepted: 5 September 2011 / Published: 15 September 2011
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.
Keywords: NMR; spectral reconstruction; sparsity; undersampling; compressed sensing
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MDPI and ACS Style
Qu, X.; Guo, D.; Cao, X.; Cai, S.; Chen, Z. Reconstruction of Self-Sparse 2D NMR Spectra from Undersampled Data in the Indirect Dimension. Sensors 2011, 11, 8888-8909.
Qu X, Guo D, Cao X, Cai S, Chen Z. Reconstruction of Self-Sparse 2D NMR Spectra from Undersampled Data in the Indirect Dimension. Sensors. 2011; 11(9):8888-8909.
Qu, Xiaobo; Guo, Di; Cao, Xue; Cai, Shuhui; Chen, Zhong. 2011. "Reconstruction of Self-Sparse 2D NMR Spectra from Undersampled Data in the Indirect Dimension." Sensors 11, no. 9: 8888-8909.