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

Application of Advanced Singular Value Decomposition Algorithm to Time Domain Transient Electromagnetic Signal De-noising

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,本文算法考察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。

In the singular value decomposition de-noising algorithm, the choice of the effective rank order is of great impor- tance 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 exist- ing rank-determining algorithms, the proposed method cares about the peaks but not the maximum of the normalized differ- ence, chooses the appropriate peak and determines the rank order together with the difference ratio of the singular value se- quence. In simulation experiments we found that for two similar peaks of the singular value difference,the one whose differ- ence ratio is smaller, is more appropriate to be the effective rank order. The proposed method can keep the waveform fea- ture of the desired signal and decrease distortion while de-noising.