Liu Huan, Dong Haobin, Ge Jian, Liu Zheng, Yuan Zhiwen, Zhu Jun, Zhang Haiyang
School of Automation, China University of Geosciences, Wuhan, Hubei 430074, China.
School of Engineering, University of British Columbia Okanagan Campus, Kelowna, British Columbia V1V 1V7, Canada.
Rev Sci Instrum. 2019 Mar;90(3):035116. doi: 10.1063/1.5089582.
The free induction decay (FID) transversal data determines the measurement accuracy of time-dependent geomagnetic fields, whereas the conservation of clean components and removal of noise cannot be easily achieved for this kind of data. Even though numerous techniques have been proven to be effective in improving the signal-to-noise ratio by filtering out frequency bands, how to efficiently reduce noise is still a crucial issue due to several restrictions, e.g., prior information requirement, stationary data assumption. To end this, a new multivariate algorithm based on the fusion of principal component analysis (PCA) and singular value decomposition (SVD), namely, principal component analysis and decomposition (PCAD), was presented. This novel algorithm aims to reduce noise as well as cancel the interference of FID transversal data. Specifically, the PCAD algorithm is able to obtain the dominant principal components of the FID and that of the noise floor by PCA, in which an optimal number of subspaces could be retained via a cumulative percent of variance criterion. Furthermore, the PCA was combined with an SVD filter whose singular values corresponding to the interferences were identified, and then the noise was suppressed by nulling the corresponding singular values, which was able to achieve an optimum trade-off between the preservation of pure FID data and the denoising efficiency. Our proposed PCAD algorithm was compared with the widely used filter methods via extensive experiments on synthetic and real FID transversal data under different noise levels. The results demonstrated that this method can preserve the FID transversal data better and shows a significant improvement in noise suppression.
自由感应衰减（FID）横向数据决定了随时间变化的地磁场的测量精度，然而对于这类数据，要实现干净成分的保留和噪声去除并非易事。尽管已证明许多技术通过滤除频段在提高信噪比方面有效，但由于一些限制，如先验信息要求、平稳数据假设等，如何有效降低噪声仍是一个关键问题。为此，提出了一种基于主成分分析（PCA）和奇异值分解（SVD）融合的新多元算法，即主成分分析与分解（PCAD）。这种新颖的算法旨在降低噪声并消除FID横向数据的干扰。具体而言，PCAD算法能够通过PCA获得FID的主导主成分和本底噪声的主成分，其中可通过方差累积百分比准则保留最优数量的子空间。此外，将PCA与一个SVD滤波器相结合，识别出对应干扰的奇异值，然后通过使相应奇异值归零来抑制噪声，这能够在保留纯FID数据和去噪效率之间实现最佳权衡。通过在不同噪声水平下对合成和真实FID横向数据进行广泛实验，将我们提出的PCAD算法与广泛使用的滤波方法进行了比较。结果表明，该方法能更好地保留FID横向数据，并且在噪声抑制方面有显著改进。
