Scale and rotation statistic-based self-adaptive function for ground penetrating radar denoising in curvelet domain

Li Jing-He; He Zhan-Xiang; Yang Jun; Meng Shu-Jun; Li Wen-Jie; Liao Xiao-Qian

doi:10.7498/aps.68.20182061

Abstract

Nonlinear and non-stationary ground penetrating radar (GPR) data for geophysics exploration are often mixed with various complex noise sources, such as random and coherent noise. Those complex noise sources are introduced by the acquisition system and other sources of measurement uncertainty. The data sets which are contaminated by the above noises have a serious influence on the accurate extraction of weak reflected signals and the effective identification of diffracted wave hyperbolic coaxial characteristics. The ignorance of the influence of noise will cause great errors in the interpretation of GPR data and the subsequent migration imaging with full waveform. The curvelet transform not only is related to position and frequency as compared with the wavelet transform, but also is controlled by the translation angle. With such a unique advantage, curvelets are used for ground roll whitening, coherent noise denoising and separation of overlapping events. The traditional curvelet transform denoising with a hard threshold function needs to give a reasonable threshold function control coefficient according to the noise level of GPR data. As a result, an appropriate choice of a hard threshold is a basic requirement, and this presents a challenging task in curvelet denoising. To overcome these shortcomings, an self-adaptive threshold function for GPR data denoising with curve transform is proposed in this paper. For detailing the reasonable control coefficient of the threshold function, the complex block threshold function algorithm is used to analyze the distribution of peak-signal-to-noise ratio value of the noisy synthetic GPR data contaminated with random and coherent noise by using the traditional threshold function curvelet transform. Based on the high order statistical theory, the accuracy distribution of the curvelet coefficient for useful signals in scale and rotation direction are correlatively stacked and determined by using the statistical self-adaptive function. And then the threshold range of noise removal components is given by the statistical self-adaptive function. The effectiveness of the proposed denoising algorithm for the noisy synthetic contaminated with different types of noise (i.e., Gaussian random and coherent), and field GPR data is demonstrated by comparing the denoising results via curvelet transform with those from traditional thresholding function. The presented denoising results by the statistical self-adaptive function is helpful and instructive for the accurate inference and interpretation of complex GPR data.

Keywords:

Authors and contacts

1.
College of Earth Sciences, Guilin University of Technology, Guilin 541004, China
2.
Department of Earth and Space Sciences, Southern University of Science and Technology, Shenzhen 518055, China

Corresponding author: Yang Jun, lijinghe7513@163.com

Funds: Project supported by the Natural Science Foundation of Guangxi Province, China (Grant Nos. 2018GXNSFAA281028, 2016GXNSFBA380195), the National Natural Science Foundation of China (Grant No. 41604097), the Research Foundation from Guilin University of Technology, China (Grant No. 002401003503), and the Nonferrous Metal Hidden Heposit Exploration and Material Development Collaborative Innovation Center Project of Guangxi Province, China (Grant No. GXYSXTZX2017-Ⅱ-5).

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References

[1]	李雪萍, 纪奕才, 卢伟, 方广有 2014 63 044201 Google Scholar Li X P, Ji Y C, Lu W, Fang G Y 2014 Acta Phys. Sin. 63 044201 Google Scholar
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Cited By

图 1 含噪声模拟合成探地雷达数据的曲波变换阈值去噪结果　(a)原始合成数据; (b)含随机噪声数据, PSNR = 17 dB; (c)含相关噪声数据, PSNR = 15.51 dB; (d)去噪数据PSNR值随阈值控制系数δ的变化

Figure 1. Denoised results for the synthetic ground penetrating radar (GPR) data with random and coherent noise using traditional curvelet transform: (a) Original GPR data; (b) data with random noise, PSNR = 17 dB; (c) data with coherent noise, PSNR = 15.51 dB; (d) the δ value vs. PSNR value curves

DownLoad: Full-Size Img PowerPoint

图 2 δ = 0.08时含噪声数据(图1(b)和图1(c))曲波变换去噪结果　(a)随机噪声数据去噪结果, PSNR = 20.23 dB, 提高3.23 dB; (b)相关噪声数据去噪结果, PSNR = 16.75 dB, 提高1.24 dB

Figure 2. Denoised results for the synthetic GPR data (Fig. 1. (b) and Fig. 1. (c)) with δ = 0.08 using traditional curvelet transform: (a) Result for random noise, PSNR = 20.23 dB; (b) result for coherent noise, PSNR = 16.75 dB.

DownLoad: Full-Size Img PowerPoint

图 3 含噪声数据(图1(b)和图1(c))的统计量自适应阈值曲波变换去噪结果　(a)随机噪声数据去噪结果, PSNR = 25.3 dB, 提高8.3 dB; (b)相关噪声数据去噪结果, PSNR = 21.92 dB, 提高6.41 dB

Figure 3. Denoised results for the synthetic GPR data (Fig. 1. (b) and Fig. 1. (c)) using curvelet transform with statistical self-adaption: (a) Result for random noise, PSNR = 25.3 dB; (b) result for coherent noise, PSNR = 21.92 dB.

DownLoad: Full-Size Img PowerPoint

图 4 双矩形目标模型含噪声数据统计量自适应阈值曲波变换去噪结果　(a)原始合成数据; (b)含随机噪声数据, PSNR = 16.04 dB; (c)含相关噪声数据, PSNR = 15.7 dB; (d)随机噪声数据去噪结果, PSNR = 23.97 dB; (e)相关噪声数据去噪结果, PSNR = 21.05 dB

Figure 4. Denoised results for the synthetic GPR data of complex model with random and coherent noise using curvelet transform with statistical self-adaption: (a) Original GPR data; (b) data with random noise, PSNR = 16.04 dB; (c) data with coherent noise, PSNR = 15.7 dB; (d) result for random noise, PSNR = 23.97 dB; (e) result for coherent noise, PSNR = 21.05 dB.

DownLoad: Full-Size Img PowerPoint

图 5 双矩形目标模型含噪声数据第50道统计量自适应阈值曲波变换去噪结果　(a)随机噪声数据去噪结果; (b)相关噪声数据去噪结果

Figure 5. Denoised results for the synthetic GPR data (Fig. 4.) in the 50th receiver using curvelet transform with statistical self-adaption: (a) Result for random noise; (b) result for coherent noise.

DownLoad: Full-Size Img PowerPoint

图 6 实测探地雷达时间剖面传统曲波变换去噪和本文去噪算法处理结果　(a)实测时间剖面; (b)采用L2标准方差估计阈值曲波去噪结果; (c)统计量自适应阈值曲波去噪结果

Figure 6. Denoised results for field GPR data using curvelet transform with L2 standard deviation and statistical self-adaption respectively: (a) Original field GPR data; (b) result using curvelet transform with L2 standard deviation; (c) result using curvelet transform with statistical self-adaption.

DownLoad: Full-Size Img PowerPoint

图 7 实测探地雷达时间剖面第200道传统曲波变换去噪和本文去噪算法处理结果

Figure 7. Denoised results for field GPR data (Fig. 6) in the 200th receiver using curvelet transform with L2 standard deviation and statistical self-adaption respectively.

DownLoad: Full-Size Img PowerPoint

map

[1]	李雪萍, 纪奕才, 卢伟, 方广有 2014 63 044201 Google Scholar Li X P, Ji Y C, Lu W, Fang G Y 2014 Acta Phys. Sin. 63 044201 Google Scholar
[2]	阮超, 陈小莉, 田茂 2015 电子测量技术 38 113 Google Scholar Ruan C, Chen X L, Tian M 2015 Elect. Meas. Tech. 38 113 Google Scholar
[3]	王大为, 王召巴 2018 67 210501 Google Scholar Wang D W, Wang Z B 2018 Acta Phys. Sin. 67 210501 Google Scholar
[4]	郑晶, 余可, 王鹏越, 蒋书琦, 滕星智 2017 矿业学学报 2 228 Zheng J, Yu K, Wang P Y, Jiang S Q, Teng X Z 2017 J. Mining Sci. Tech. 2 228
[5]	王磊, 陆珉, 黄春琳, 李禹 2009 信号处理 25 522 Wang L, Lu M, Huang C L, Li Y 2009 Signal Process 25 522
[6]	Jeng Y, Li Y W, Chen C S, Chien H Y 2009 J. Appl. Geophys. 68 36 Google Scholar
[7]	张先武, 高云泽, 方广有 2013 地球 56 309 Google Scholar Zhang X W, Gao Y Z, Fang G Y 2013 Chin. J. Geophys. 56 309 Google Scholar
[8]	尹柏强, 何怡刚, 吴先明 2013 62 148702 Google Scholar Yin B Q, He Y G, Wu X M 2013 Acta Phys. Sin. 62 148702 Google Scholar
[9]	张先武, 高云泽, 方广有 2013 地球 56 2790 Google Scholar Zhang X W, Gao Y Z, Fang G Y 2013 Chin. J. Geophys. 56 2790 Google Scholar
[10]	Wei X, Zhang Y 2015 IEEE J. Stars 8 1145
[11]	Wang X, Liu S 2017 Signal Process 132 227 Google Scholar
[12]	高国荣, 刘艳萍, 潘琼 2012 61 139701 Google Scholar Gao G R, Liu Y P, Pan Q 2012 Acta Phys. Sin. 61 139701 Google Scholar
[13]	王超, 沈斐敏 2015 物探与化探 39 421 Google Scholar Wang C, Shen F M 2015 Geophys. Geochem. Explor. 39 421 Google Scholar
[14]	Ghozzi R, Lahouar S, Souani C, Besbes K 2017 Advanced Systems and Electric Technologies International Conference Hammamet, Tunisia, January 14−17, 2017 p34
[15]	Tzanis A 2013 J. Appl. Geophys. 8948
[16]	Tzanis A 2015 J. Appl. Geophys. 115 145 Google Scholar
[17]	Candès E, Donoho J D L 2004 Commun. Pur. Appl. Math. 57 219 Google Scholar
[18]	Candès E, Demanet L, Donoho D, Ying L X 2006 Multiscale Model. Sim. 5 861 Google Scholar
[19]	张华, 陈小宏 2013 地球 56 1637 Google Scholar Zhang H, Chen X H 2013 Chin. J. Geophys. 56 1637 Google Scholar
[20]	董烈乾, 李培明, 张奎, 汪长辉, 祝杨, 王泽 2015 地球 58 3780 Dong L Q, Li P M, Zhang K, Wang C H, Zhu Y, Wang Z 2015 Chin. J. Geophys. 58 3780
[21]	齐少华, 刘启元, 陈九辉, 郭飚 2016 地球 59 884 Google Scholar Qi S H, Liu Q Y, Chen J H, Guo B 2016 Chin. J. Geophys. 59 884 Google Scholar
[22]	张华, 王冬年, 李红星, 黄光南, 陈晓 2017 地球 60 4480 Google Scholar Zhang H, Wang D N, Li H X, Huang G N, Chen X 2017 Chin. J. Geophys. 60 4480 Google Scholar
[23]	Neelamani R, Baumstein A I, Gillard D G 2008 Lea. Ed. 27 240 Google Scholar
[24]	张金良, 鲁昌华, 杨道莲 2013 电子测量与仪器学报 26 1108 Zhang J L, Lu C H, Yang D L 2013 J. Elect. Meas. Inst. 26 1108
[25]	Terrasse G, Nicolas J M, Trouvé E, Drouet E 2017 IEEE J. Stars 10 4280
[26]	朱自强, 朱贺, 鲁光银, 王凡, 谭洁 2014 物探化探计算技术 36 571 Google Scholar Zhu Z Q, Zhu H, Lu G Y, Wang F, Tan J 2014 Comp. Tech. Geophys. Geochem. Explor. 36 571 Google Scholar
[27]	Bao Q Z, Li Q C, Chen W C 2014 Appl. Geophys. 11 301 Google Scholar
[28]	Tzanis A 2017 Signal Process 132 243 Google Scholar
[29]	雷林林, 刘四新, 傅磊, 吴俊军 2015 地球 58 3346 Google Scholar Lei L L, Liu S X, Fu L, Wu J J 2015 Chin. J. Geophys. 58 3346 Google Scholar
[30]	Saha M, Naskar M K, Chatterji B N 2015 IETE J. Res. 61 186 Google Scholar

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