基于近似l0范数最小化的NMR波谱稀疏重建算法

波谱学杂志

基于近似l₀范数最小化的NMR波谱稀疏重建算法

张正炎，屈小波，林雁勤*，陈忠

厦门大学电子科学系，福建省等离子体与磁共振研究重点实验室，福建厦门 361005

收稿日期:2013-04-24 修回日期:2013-05-27 出版日期:2013-12-05 发布日期:2013-12-05
作者简介:张正炎(1986-)，男，安徽人，硕士研究生，主要从事压缩传感研究.*通讯联系人：林雁勤，电话：0592-2183301, E-mail: linyq@xmu.edu.cn.
基金资助:
国家自然科学基金资助项目（11105114、11174239和61201045），中央高校基本科研业务费资助项目（2010121010）.

A Sparse Reconstruction Algorithm for NMR Spectroscopy Based on Approximate l₀ Norm Minimization

ZHANG Zheng-yang，QU Xiao-bo，LIN Yan-qin*，CHEN Zhong

Department of Electronic Science, Fujian Key Laboratory of Plasma and Magnetic Resonance, Xiamen University, Xiamen 361005, China

Received:2013-04-24 Revised:2013-05-27 Online:2013-12-05 Published:2013-12-05
About author:*Corresponding author: Lin Yan-qin, Tel: 0592-2183301, E-mail: linyq@xmu.edu.cn.
Supported by:
国家自然科学基金资助项目（11105114、11174239和61201045），中央高校基本科研业务费资助项目（2010121010）.

摘要/Abstract

摘要：

在核磁共振（NMR）波谱中，过长的数据采集时间会使很多化学以及分子生物学领域的高分辨率多维谱应用难以实现. 传统的解决办法是使用随机非均匀采样代替奈奎斯特采样，但这样会使谱图质量受损. 压缩传感的出现为此提供了更好的解决办法，合适的压缩传感重建算法可以通过很少的随机非均匀采样将谱图高质量的重建出来. 该文先介绍了一种可用于谱图重建的压缩传感重建算法，名为“平滑l₀范数最小化法”，然后针对该算法对采样噪声鲁棒性较差的缺点进行了改进. 通过将改进后的算法与原算法在一维实数域信号以及NMR波谱信号重建实验中进行对比后表明，改进后的算法对噪声的鲁棒性明显提高，并能获得更好的重建性能.

关键词: NMR波谱, 压缩传感, 近似l₀范数, 迭代重复加权, 信噪比

Abstract:

Long acquisition time often hinders the routine application of multidimensional NMR spectroscopy. A common approach to reduce the acquisition time is to replace the commonly used Nyquist grid sampling scheme with a random non-uniform sampling (NUS) scheme. However, NUS is inherently associated with degradation of spectrum quality. It has been demonstrated recently compressed sensing (CS) algorithms can be used to reconstruct highquality spectra from sparse NUS data. In this paper, a CS reconstruction algorithm called “Smoothed l₀ Norm Minimization” was introduced. The typical version of the algorithm was then-modified to improve its robustness under high noise condition. The improved algorithm was applied to reconstruct 1D realvalued signal and 2D NMR spectroscopy, and the results were compared with those obtained by other methods. The results showed that the algorithm proposed had better robustness to noise, and could be used to reconstruct high-quality spectra with fewer sampling data.


Key words: NMR spectroscopy, compressed sensing, approximate l₀norm, re-weighted, signal-to-noise ratio

中图分类号:

O482.53

张正炎，屈小波，林雁勤*，陈忠. 基于近似l₀范数最小化的NMR波谱稀疏重建算法[J]. 波谱学杂志.

ZHANG Zheng-yang，QU Xiao-bo，LIN Yan-qin*，CHEN Zhong. A Sparse Reconstruction Algorithm for NMR Spectroscopy Based on Approximate l₀ Norm Minimization[J]. Chinese Journal of Magnetic Resonance.

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基于近似l₀范数最小化的NMR波谱稀疏重建算法

A Sparse Reconstruction Algorithm for NMR Spectroscopy Based on Approximate l₀ Norm Minimization

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