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非线性、非平稳探地雷达数据常掺杂各种复杂噪声源, 其对精确提取弱反射波信号、识别绕射波双曲线同相轴特征具有严重影响, 忽略噪声影响给探地雷达探测数据全波形偏移成像及后续解译造成较大误差. 采用传统阈值函数的曲波变换去噪需要根据数据噪声水平人为确定合理阈值控制系数. 对此, 本文开展自适应阈值函数的曲波变换去噪算法研究. 引入块状复数域阈值函数算法, 分析传统阈值函数曲波变换去噪的效果随阈值控制系数变化的规律; 利用高阶统计量理论, 对曲波变换系数在尺度、方向上进行相关性叠加, 通过相关性统计量自适应确定有效信号在曲波变换系数分布尺度、旋转方向, 由此确定清除噪声成分阈值范围, 构建统计量自适应阈值函数曲波变换去噪算法. 针对包含随机噪声、相关噪声合成探地雷达数据及实测探地雷达数据, 采用传统阈值函数曲波变换去噪与本文提出去噪算法处理结果对比分析, 检验了本文算法的有效性及可行性. 研究成果对复杂探地雷达数据精确推断解译具有指导意义.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.
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Keywords:
- ground penetrating radar denoising /
- self-adaptive thresholding function /
- statistic /
- curvelet transform
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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
Fig. 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
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
Fig. 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.
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
Fig. 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.
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
Fig. 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.
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
Fig. 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.
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
Fig. 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.
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
Fig. 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.
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[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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