改进奇异值分解算法在时间域瞬变电磁信号降噪中的应用

奇异值分解降噪算法中，有效秩阶次的判断对降噪算法的性能的影响至关重要。为选取更准确的有效秩阶次，本文研究了奇异值序列的差分，提出判断奇异值分解重构的有效秩阶次的新方法，并应用其对时间域瞬变电磁信号降噪，提高输出信号的信噪比。与现有判断有效秩阶次的算法不同，本文算法考查奇异值序列的归一化差分的峰值而不是最大值，通过选择归一化差分的合适峰值，并综合差分比序列以判断阶次。实验中发现，对于两个大小相近的尖峰，其中差分比小的，更适合作为有效秩阶次。本文算法在降噪的同时，能较好地保留有用信号的波形特征，减小失真。 

Application of advanced singular value decomposition algorithm for time domain transient electromagnetic signal denoising

In the singular value decomposition de-noising algorithm, the choice of the effective rank order is of great importance to influence the performance of the de-noising algorithm. To select a more accurate effective rank order, this paper studied the difference of singular value sequence, proposed a new method to determine the effective rank order, applied it to de-noise the time domain transient electromagnetic signal, and raised the output signal-to-noise ratio. Differs from existing rank-determining algorithms, the proposed method cares about the peaks but not the maximum of the normalized difference, chooses the appropriate peak and determines the rank order together with the difference ratio of the singular value sequence. In simulation experiments we found that for two similar peaks of the singular value difference ,the one whose difference ratio is smaller, is more appropriate to be the effective rank order . The proposed method can keep the waveform feature of the desired signal and decrease distortion while de-noising.