小波包多阈值去噪法及其在形变分析中的应用

摘要/Abstract

摘要：

在GPS变形监测领域，传统的小波去噪只保留低频上的有用信息，很容易去掉中频以及高频上的有用信息。小波包分析方法是近几年发展起来的一种新的小波分析方法，它同时考虑了各个频段上的有用信息，因此是一种更为精细的去噪方法。小波包去噪的关键是对小波包分解系数选取合适的阈值准则并进行阈值处理，但传统的小波包去噪并没有对此进行充分的研究。本文针对传统小波、小波包分析的不足，提出了一种基于频率顺序并依据信息类型分段的多阈值准则小波包去噪法。通过理论分析与实际应用，结果表明新方法能够高效剔除各频段的噪声，同时当采样频率较低时能有效保留去噪信号中频率高达10-1 Hz数量级的有用信息，其去噪能力优于传统的小波、小波包等其它去噪方法，因此可以广泛应用于高精度GPS变形监测领域中。

关键词: 小波包分析, 变形监测, 数据去噪, 频率顺序, 多阈值准则

Abstract:

In the field of GPS deformation monitoring, the traditional wavelet de-noising method retains only the low frequency of useful information. It is easy to get rid of intermediate frequency and high frequency useful information. The wavelet packet analysis is a new kind of wavelet analysis method developed in recent years, which is a more subtle de-noising method for considering useful information of the various bands. The key of the wavelet packet de-noising is to select the appropriate threshold criteria and to process the wavelet packet decomposition coefficients by the threshold, but the researches using traditional wavelet packet de-noising method is not sufficient. This article is for the lack of traditional wavelet and wavelet packet analysis. According to the distribution of different signals and their noise, wavelet packet decomposition coefficients are arranged by the frequency order, and segmented in accordance with information type, to select the appropriate threshold criteria for each band and to perform threshold processing. It is the method of wavelet packet de-noising with multi-threshold criteria based on frequency order. The results show that this new method can effectively remove the noise of each band through theoretical analysis and practical applications. The de-noising ability of this method is better than the other methods such as traditional wavelet de-noising or wavelet packet de-noising. Studies have shown that this method can valid preserve the frequency 10-1 Hz magnitude of useful information from the de-noising signal after de-noising when the sampling frequency is low. Therefore, it can be widely used in the field of high-precision GPS deformation monitoring.

Key words: wavelet packet analysis, deformation monitoring, data de-noising, frequency order, multi-threshold criteria

中图分类号:

P207

章浙涛朱建军匡翠林周璀. 小波包多阈值去噪法及其在形变分析中的应用[J]. 测绘学报, 2014, 43(1): 13-20.

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