﻿ 基于小波变换与主成分分析的探地雷达自适应杂波抑制方法研究
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 雷达学报  2015, Vol. 4 Issue (4): 445–451  DOI: 10.12000/JR15013 0

### 引用本文 [复制中英文]

[复制中文]
Qin Yao, Huang Chun-lin, Lu Min, et al.. Adaptive clutter reduction based on wavelet transform and principal component analysis for ground penetrating radar[J]. Journal of Radars, 2015, 4(4): 445–451. DOI: 10.12000/JR15013.
[复制英文]

### 文章历史

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Adaptive Clutter Reduction Based on Wavelet Transform and Principal Component Analysis for Ground Penetrating Radar
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School of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China;
Engineer Academy of People’s Liberation Army, Xuzhou 221000, China
Foundation Items: The National Natural Science Foundation of China (61372160);The Foundation for Doctoral Supervisor of China (20134307110011)
Abstract: Because of the limitations of traditional Principal Component Analysis (PCA) in clutter reduction, an improved PCA subspace method is proposed based on the 2D wavelet transform. Moreover, the combination of the improved subspace method and adaptive filtering ensures the signal fidelity and learning adaptability of adaptive filtering. Then, an adaptive clutter reduction algorithm based on wavelet transform and PCA, as well as adaptive filtering, is proposed. The experimental results suggest that the proposed method improves the signal to clutter ratio and target image definition.
Key words: Ground Penetrating Radar (GPR)     Clutter reduction     Principal Component Analysis (PCA)     Wavelet transform     Adaptive filtering
1 引言

 ${W_{\rm R}} = UD{V^T} = \sum\limits_{i = 1}^P {{u_i}{D_{i,i}}v_i^T}, P = min\{ M,N\}$ (1)

 $l = \sum\limits_{j = 1}^r {{D_{i,i}}} /\sum\limits_{i = 1}^P {{D_{i,i}}}$ (2)

(1) 对原始探地雷达记录的回波数据进行2维小波变换，得到不同分解次数下近似值、水平细节、垂直细节与对角细节信号。小波变换分解次数决定于实际地质资料的复杂度，文中均采用一次小波分解。

(2) 对小波分解得到的不同信号进行主成分分析，取一定贡献率特征值进行重构。

(3) 对经主成分分析处理后的不同信号进行2维小波反变换。 3 自适应杂波抑制

 图 1 双边线性预测方法示意图 Fig.1 Illustration of two-sided linear prediction approach
 ${x_m} = \left[ {{x_{m - p}}{x_{m + p}}} \right]\left[ \matrix{ \theta \left( 0 \right) \hfill \cr \theta \left( 1 \right) \hfill \cr} \right] = {A_m}\hat \theta$ (3)

 $\hat \theta \left( n \right) = \hat \theta \left( {n - 1} \right) + K\left( n \right)\left( {{x_m}\left( n \right) - A_{_m}^{\rm T}\hat \theta \left( {n - 1} \right)} \right)$ (4)
 $K\left( n \right) = {{{\lambda ^{ - 1}}P\left( {n - 1} \right)A\left( n \right)} \over {1 + {\lambda ^{ - 1}}{A^{\rm T}}\left( n \right)P\left( {n - 1} \right)A\left( n \right)}}$ (5)
 $P\left( n \right) = {\lambda ^{ - 1}}P\left( {n - 1} \right) - {\lambda ^{ - 1}}K\left( n \right)A_{_m}^{\rm T}P\left( {n - 1} \right)$ (6)

 图 2 Wavelet-PCA-TSLP流程图 Fig.2 Flow of Wavelet-PCA-TSLP algorithm
4 实验结果与分析

 图 3 第1组数据的实验结果 Fig.3 Results of first B-scan targets after clutter reduction

 $\rm {SCR} = {{\sum\limits_{i = 1}^I {\sum\limits_{i = 1}^J {{T^2}\left( {i,j} \right)/\left( {IJ} \right)} } } \over {\sum\limits_{m = 1}^M {\sum\limits_{n = 1}^N {{W^2}\left( {m,n} \right)/\left( {MN} \right)} } }}$ (7)

 $Q = {{{{\left( {\sum\limits_{i = 1}^I {\sum\limits_{j = 1}^J {{T^2}\left( {i,j} \right)} } } \right)}^2}} \over {\sum\limits_{i = 1}^I {\sum\limits_{j = 1}^J {{T^4}\left( {i,j} \right)} } }}$ (8)

 图 4 第2组数据的实验结果 Fig.4 Results of second B-scan targets after clutter reduction