基于双树复小波的变形监测数据去噪分析

将双树复小波引入到变形监测数据去噪中，从信号分解、去噪过程和去噪质量3个方面综合评价其可行性和有效性。理论分析和算例表明，信噪分离的质量会对阈值估计、阈值去噪和信号重构产生较大影响，信噪分离较好的信号能在一定程度上削弱阈值函数存在的缺陷；双树复小波的分解效果优于传统离散小波，能较好地表现出细节部分的频率信息，使变形信号的周期性变化特征更为明显，可以应用于变形监测数据分析。

Deformation Analysis Based on a Dual-Tree Complex Wavelet Transform Method

The dual-tree complex wavelet is introduced into the de-noising of the deformation monitoring data. The feasibility and effectiveness are comprehensively evaluated by the signal decomposition, de-noising process and de-noising quality. The theoretical analysis and examples show that the quality of signal-to-noise separation will have a great impact on threshold estimation, threshold de-noising and signal reconstruction. To a certain extent, the signal with better signal-to-noise separation can weaken the defect of threshold function. The decomposition effect of dual-tree complex wavelet is better than that of traditional discrete wavelet, and it can better display the frequency information of the detail part, so that the characteristic variation of deformation signal is more obvious. The dual-tree complex wavelet can be applied in deformation monitoring data analysis.