«上一篇
 文章快速检索 高级检索

 雷达学报  2018, Vol. 7 Issue (3): 294-302  DOI: 10.12000/JR17113 0

### 引用本文

Lei Wentai, Liang Qiong, and Tan Qianying. A new ground penetrating radar signal denoising algorithm based on automatic reversed-phase correction and kurtosis value comparison[J]. Journal of Radars, 2018, 7(3): 294-302. DOI: 10.12000/JR17113.

### 文章历史

(中南大学信息科学与工程学院    长沙    410075)

A New Ground Penetrating Radar Signal Denoising Algorithm Based on Automatic Reversed-phase Correction and Kurtosis Value Comparison
Lei Wentai, Liang Qiong, Tan Qianying
(Institute of Information Science and Engineering, Central South University, Changsha 410075, China)
Foundation Item: The National Natural Science Foundation of China (61102139), The Graduate Independent Exploration and Innovation of Central South University (2017zzts481)
Abstract: When using Ground Penetrating Radar (GPR) on the occasion of complex underground medium detection, radar echo can be easily affected by various noise. In order to improve GPR detection resolution and data interpretation quality, this paper proposed a new GPR denoising algorithm based on automatic reversed-phase correction and kurtosis value comparison. GPR echo signal and random noise with the same length were fitted and two signals can be obtained. By using Independent Component Analysis (ICA) algorithm, these two signals can be decomposed into two other signals, one with high kurtosis named S1 and one with low kurtosis named S2. S1 signal’s phase was determined and automatic phase correction was carried out. By using Complete Ensemble Empirical Mode Decomposition (CEEMD) algorithm, S1 after automatic phase correction was decomposed, several Intrinsic Mode Function (IMF) can be obtained and kurtosis value of each IMF can be calculated. S2 signal’s kurtosis value was set as a threshold. The IMFs whose kurtosis values are lower than this threshold are classified as noise components, while the other IMFs whose kurtosis values are higher than this threshold are classified as signal components. By summing the IMFs of signal components, GPR echo signal can be reconstructed and denoising. This new GPR denoising algorithm solves the problems of phase uncertainty in ICA and manual IMF components classification in CEEMD and thus improves GPR denoising effects with higher computation efficiency. The effectiveness of the proposed algorithm is verified by simulation and real data processing experiments.
Key words: Ground Penetrating Radar (GPR)    Automatic reversed-phase correction    Kurtosis value comparison    Denoising algorithm
1 引言

2 基本原理 2.1 独立分量分析ICA

ICA是基于信号的高阶统计量，研究信号间的独立关系，将数据变换到相互独立的方向上，使经过ICA算法变换所得到的各个分量之间不仅正交，而且相互独立[12]。ICA处理的流程图如图1所示。

 图 1 ICA流程图 Fig.1 The flow diagram of ICA

2.2 完全总体经验模态分解(CEEMD)

CEEMD是一种基于EMD的通过噪声辅助的数据分析方法[1317]。将固定比例的高斯白噪声添加到原始信号中，形成新的待分解信号，对新的待分解信号进行EMD分解得到IMF分量，用不同的白噪声分别进行 $N$ 次分解，并将 $N$ 个1阶的IMF进行整体均值，即式(4)所示。

3 基于自动反相校正和峰度值比较的GPR去噪算法

 图 2 算法流程图 Fig.2 The flow diagram of the algorithm

$\alpha \cdot x'\left( m \right)$ 进行CEEMD分解，得到 $P \,$ 个IMF分量。计算每个IMF分量 ${y_p}\left( m \right),p = 1,·\!·\!·,P \,$ 的峰度值，记为 ${k_p},p = 1,·\!·\!·,P\,$ 。计算ICA算法后输出信号 $n'\left( m \right)$ 的峰度值，记为 $k$ 。因为ICA分离出的噪声 $n'\left( m \right)$ 与ICA分离出的信号 $x'\left( m \right)$ 中含有的噪声相似，所以峰度值相同 ，因为噪声是随机信号，所以信号的噪声比噪声的峰度值要大，因而将满足 ${k_p} > k$ 的所有信号分量累加，作为原始回波信号 $x\left( m \right)$ 去噪后的信号，记为

4 仿真与实测数据去噪实验

4.1 仿真数据的处理

 图 3 GPR正演模型图 Fig.3 The forward model diagram of GPR
 图 4 正演模拟得到的GPR无噪回波信号图 Fig.4 The GPR no-noise echo signal by forward modeling

 图 5 加入噪声后模拟得到的GPR含噪信号和产生的等长度的随机噪声信号 Fig.5 The GPR noise signal and the generated equal length random noise signal obtained by adding noise

 图 6 随机拟合后得到的两道信号 Fig.6 Two channel signals obtained after random fitting
 图 7 经过ICA算法后分离出的两道信号 Fig.7 Two channel signals separated by ICA algorithm

 图 8 经过CEEMD分解后的各IMF分量波形图 Fig.8 The IMF component waveform diagram after CEEMD decomposition

 图 9 各IMF分量采用峰度值阈值分类后累加重构的信号 Fig.9 The signal of cumulative reconfiguration after the IMF components classified by kurtosis threshold value

 图 10 本算法和常规算法的去噪误差和信噪比的变化曲线对比图 Fig.10 The contrast diagram of the variation curve of denoising error and signa-to-noise ratio of the algorithm and the conventional algorithm

4.2 实测数据的处理

 图 11 原始GPR B-Scan图 Fig.11 The original GPR B-Scan

 图 12 未去噪原始B-scan1和本算法去噪结果B-scan2对比图 Fig.12 The contrast diagram of the original B-Scan1 with noise and the denoising result of B-Scan2 in the present algorithm

 图 13 未去噪原始A-Scan和本算法去噪结果A-Scan对比图 Fig.13 The contrast diagram of the original A-Scan with noise and the denoising result of A-Scan in the present algorithm

5 总结

GPR回波信号的去噪处理决定着后续的数据解译质量。针对现有去噪算法的相位不确定和人工判别IMF分量的问题，本文提出基于自动反相校正和峰度值比较的去噪算法，设计了相位判别因子，实现了ICA分解后的信号相位自动判别和校正，设计了基于峰度值比较的IMF分量自动筛选，阈值选择为ICA算法分离出来的噪声信号的峰度值。该算法避免了ICA分解后的相位不定性，且在CEEMD分解后无需传统的人工方式进行各IMF分量的筛选。通过对仿真和实测数据的处理，验证了本文所提算法的有效性。后续研究工作将集中在CEEMD算法运算效率的优化上，进一步提高去噪效率。