基于近似l0范数最小化的NMR波谱稀疏重建算法

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.

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

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.
