基于低秩Hankel矩阵的核磁共振谱自动参数去噪方法
An auto-parameter denoising method for nuclear magnetic resonance spectroscopy based on low-rank Hankel matrix
摘要：
核磁共振（NMR）谱被建模为阻尼指数信号的和，在各种情况下，如结构和功能测定、化学分析和疾病诊断，它已成为不可或缺的工具。然而，NMR光谱信号，在实践中，通常被高斯噪声破坏，提高了顺序分析和量化的信号的困难。低秩Hankel性质在去噪问题中起着重要的作用，但选择合适的参数仍然是一个问题。在这项工作中，我们探讨了正则化参数的效果的凸优化去噪方法的基础上，低秩汉克尔矩阵的指数信号被高斯噪声破坏。给出了加权Hankel矩阵谱范数的精确估计，作为正则化参数设置的指导。可以有效地计算界限，因为它只取决于噪声的标准偏差和一个常数。借助于该界，可以很容易地获得自动设置的正则化参数，以产生有希望的去噪结果。我们的合成和现实的NMR光谱数据的实验表明，我们提出的方法相比，典型的Cadzow和国家的最先进的QR分解方法，特别是在低信噪比制度优越的去噪性能。
英文摘要：
Nuclear Magnetic Resonance (NMR) spectroscopy, which is modeled as the sum of damped exponential signals, has become an indispensable tool in various scenarios, such as the structure and function determination, chemical analysis, and disease diagnosis. NMR spectroscopy signals, however, are usually corrupted by Gaussian noise in practice, raising difficulties in sequential analysis and quantification of the signals. The low-rank Hankel property plays an important role in the denoising issue, but selecting an appropriate parameter still remains a problem. In this work, we explore the effect of the regularization parameter of a convex optimization denoising method based on low-rank Hankel matrices for exponential signals corrupted by Gaussian noise. An accurate estimate on the spectral norm of weighted Hankel matrices is provided as a guidance to set the regularization parameter. The bound can be efficiently calculated since it only depends on the standard deviation of the noise and a constant. Aided by the bound, one can easily obtain an auto-setting regularization parameter to produce promising denoised results. Our experiments on synthetic and realistic NMR spectroscopy data demonstrate a superior denoising performance of our proposed approach in comparison with the typical Cadzow and the state-of-the-art QR decomposition methods, especially in the low signal-to-noise ratio regime.
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