Application of the prediction deconvolution technique to signal processing in ground penetrating radar systems

In the paper, will propose the prediction deconvolution technique for signal processing in GPR systems. The technique is developed based on the method of Least Square filter and Wiener filter. Our processed results have shown that by applying the proposed technique, received signals will be eliminated interference and give better images with high resolution.

Science & Technology Development, Vol 15, No.K1- 2012 APPLICATION OF THE PREDICTION DECONVOLUTION TECHNIQUE TO SIGNAL PROCESSING IN GROUND PENETRATING RADAR SYSTEMS Le Van Hung(1), Bui Huu Phu(2), Nguyen Thanh Duy(2), Nguyen Thanh Nam(2) (1) University of Industry of Hochiminh City (2) DCSELAB, University of Technology, VNU-HCM (Manuscript Received on April 5th, 2012, Manuscript Revised November 20rd, 2012) ABSTRACT: Ground penetrating radar (GPR) systems emit electromagnetic energy into ground and receive reflection signals to process and display images of objects underground The technology can be applied to variety of fields such as military, constructions, geophysics, In the paper, we will propose the prediction deconvolution technique for signal processing in GPR systems The technique is developed based on the method of Least Square filter and Wiener filter Our processed results have shown that by applying the proposed technique, received signals will be eliminated interference and give better images with high resolution In addition, to get good results we see that it is necessary to predict the accuracy of pulse response of environments Keywords: Prediction Deconvolution Technique, Signal Processing, Ground Penetrating Radar (GPR) characteristics INTRODUCTION Ground penetrating radar (GPR) technology has been widely studied over the world The GPR system emits electromagnetic energy into ground and receives reflection signals to process and display images of objects underground The technology can be applied to of material underground, received signals are widen and delayed responses, thus reduce the resolution of GPR’s image The purpose of the deconvolutional techniques is to convert the responses into a narrow pulse in order to eliminate interference and improve the resolution [1, 2, 5] variety of fields such as detection of buried Signal processing techniques until now mines, mine detection (gold, oil, underground have been used techniques of image processing water, ), pipes and cable detection, evaluation such as noise removal, smooth processing by of geophysical two dimensional multiplication convolution, or investigations, road condition survey, tunnel & median filter, [12] However, for GPR wall condition, [1-11] signals, we need to not only process images but reinforced concrete, In GPR systems, transmitted signals are narrow pulses Due to interference and also recover transmitted narrow pulses In the paper, we propose a method of prediction deconvolution, which can two simultaneous Trang 52 TẠP CHÍ PHÁT TRIỂN KH&CN, TẬP 15, SỐ K1- 2012 tasks of prediction and deconvolution The characteristics results of processing are much dependent on without dig and destruction The model of GPR the prediction distance The importance of the systems is shown in Fig The system uses deconvolution technique is to process widen high signals to a spike pulse Therefore, the information underground Signals transmitted technique can eliminate Gaussian noise and from antennas penetrate into ground with a recover signals in time domain and increase the velocity depended on environments When the resolution of GPR’s images The technique is signals go through different layers of material based on the method of Least Square filter and with different dielectrical constants, a part of Wiener filter Our processed results have the signals is reflected Receive antennas shown that by applying the proposed technique, receive the signals and then process to view the received signals will be eliminated interference images Because the reflected signals are and give better images with high resolution In created at the border of material layers, by addition, to get good results we see that it is processing, viewing, and monitoring, we can needed to predict the accuracy of pulse determine the structure and shape of objects response of environments underground The remaining of the paper is organized as follows In the next section, the model of GPR systems is described The proposed technique of predict convolution is presented in section In section 4, we show the process of the technique and discuss its results Finally, we conclude the paper in section frequency THE of materials radio PREDICT signals underground to collect CONVOLUTION TECHNIQUE Signal processing plays an important part in GPR systems The purpose of the signal processing techniques is to eliminate noise and interference, improve the quality of images, and locate the position of desired targets In the MODEL OF GPR SYSTEMS paper, we propose a prediction deconvolution technique, which efficiently eliminates noise and interference, improve the quality of images The proposed technique is developed based on a consequence of filters: Invert filter, Least Square filter, and Weiner filter 3.1 Invert filter A concept of invert filter is shown in Fig.2 If w(t) is GPR wavelet signals received and δ(t) Fig Block diagram of a GPR system GPR is a method applied electromagnetic energy to investigate structures and is desired output signals, then f(t) must satisfy the below condition: Trang 53 Science & Technology Development, Vol 15, No.K1- 2012 δ (t ) = w (t ) ∗ f (t ) or f (t ) = δ (t ) ∗ (1) w(t ) By conducting z-transform of (1), we have F ( z) = = f + f1 z + f z + W (z) Where W ( z ) = w0 + w1 z + w2 z + (2) (3) error between signals y(t) and desired signals d(t) as: arg || e(t ) || = arg || d (t ) − y (t ) || (5) f1 , f , , f n f1 , f , , f n After receiving the coefficients, the filter deconvolutes again with GPR received signals to get output signals The expression shows the determination of the filter’s coefficients by inverting the ztransform of GPR wavelet However, the filter usually gives enormous error, especially when GPR wavelet signals are different from desired signals Fig Least Square Filter According to [12], the method is significantly dependent on the initial phase of desired signal d(t) If the phase is small, then the error is small; and if the phase is large, then Fig Invert Filter the error is large In addition, the method is quite complex when the order of filter is high 3.2 Least square filter 3.3 Weiner filter This is the method to find the filter’s coefficients so that the difference between A concept of Weiner filter is shown in Fig received signals and the desired signals is Assuming that received signals are (x0, minimal A concept of Least Square filter is x1,…,xn-1), desired signals are (d0, d1, …dn-1) shown in Fig The filter’s coefficients f1, f2,…,fn are initial with arbitrary values, then convolute with GPR received signals w(t) as: The autocorrelation of received signals (r0 ,r1 ,…rn-1) is given by rτ = ∑ x(t ) x(t − τ ) t y(t) = w(t) * f(t) (4) Then, the coefficients are determined by applying the least square error algorithm for the Trang 54 for n=5 we have: (6) TẠP CHÍ PHÁT TRIỂN KH&CN, TẬP 15, SỐ K1- 2012 3.4 Prediction deconvolution filter r0 = x02 + x12 + x22 + x32 + x42 r1 = x0 x1 + x1 x2 + x2 x3 + x3 x4 r2 = x0 x2 + x1 x3 + x2 x4 For the technique, the coefficients of the filter are determined so that output signals will r3 = x0 x3 + x1 x4 be prediction signals considering as input r4 = x0 x4 signals in future A concept of the proposed r5 = filter is shown in Fig Assuming that input (7) The cross-correlation of received signals (g0, g1,…, gn-1) is calculated as follows: g (τ ) = ∑ x(t ) d (t − τ ) (8) t prediction signals are x (t + α ) :( x2 , x3 , x4 ) with α = The coefficients of the filter are determined by solving the linear equations The coefficients of Weiner filter (a0, below: a1,…,an-1) can be determined by solving the r (α + τ ) = below equations:  r0   r1  r2  M r  n −1 r1 r0 r1 M rn −2 ∑ x (t ) x (t + α − τ ) t rn −1  a0   g      r1 L rn −  a1   g1  r0 L rn −3  a2  =  g      M O M  M   M  rn −3 L r0   an −1   g n −1  r2 are x (t ) :( x0 , x1 , x2 , x3 , x4 ) , signals (10) L (9) After receiving the coefficients, the filter Or  r0   r1  r2  M r  n−1 deconvolutes again with GPR received signals to get output signals r1 r0 r1 M rn−2 (11) rn−1   a0   rα      r1 L rn−2   a1   rα +1  r0 L rn−3   a2  =  rα +2      M O M  M   M  rn−3 L r0   an−1   rα +n−1  r2 L Now, consider special case α=1, n=5 we have  r0   r1  r2   r3 r  r1 r2 r3 r4 r0 r1 r2 r3 r1 r0 r1 r2 r2 r1 r0 r1 r3 r2 r1 r0   a0   r1        a1   r2    a2  =  r3        a3   r4        a4   r5  (11-a) By augmenting the right side to the left side we obtain Fig Wiener Filter application for GPR data Trang 55 Science & Technology Development, Vol 15, No.K1- 2012  −r1   −r2  −r   −r4  −r  r0 r1 r2 r3 r4 r1 r0 r1 r2 r3 r2 r1 r0 r1 r2 r3 r2 r1 r0 r1 r4 r3 r2 r1 r0 1     0   a0     a   0   =  0   a2       0   a3     a   0  4 (11-b) After changing and rearranging the equations, we have new equations as follows:  r0   r1  r2   r3 r 4 r 5 r1 r2 r3 r4 r0 r1 r2 r3 r1 r0 r1 r2 r2 r1 r0 r1 r3 r2 r1 r0 r4 r3 (12) r2 r1 where r5  b0   L    r4  b1      r3  b2      =   r2  b3    r1  b4        r0   b5    Fig Prediction deconvolution filter SIMULATION RESULTS b0 = 1, bi = − i = 1, 2, 3, 4,5 , L=r0-r1a0-r2a1-r3a2-r4a3-r5a4 In the section, we apply the prediction deconvolution filter to a real GPR data From equations (12), we see that prediction obtained by Malags systems [13] The deconvolution filter is based on signals in technique is carried out by using Matlab current time and received signals in future software The results are compared with time When determining the coefficients of original data to evaluate the proposed filter Weiner The structure of GPR data includes 510x2147 filter, we can also know the coefficients of prediction deconvolution filter data matrices, where 510 is data obtained in time domain, and 2147 is the numbers of traces obtained in different positions Fig Original data without processing Trang 56 TẠP CHÍ PHÁT TRIỂN KH&CN, TẬP 15, SỐ K1- 2012 Fig Apply the prediction deconvolution filter to Fig 11 Apply the prediction deconvolution filter to data with length of filter L = 3ns, prediction range data with length of filter L = 5ns, prediction range α = 5ns, and whitening ratio W=2% α = 2ns, and whitening ratio W=1% Fig Apply the prediction deconvolution filter to Fig 12 Apply the prediction deconvolution filter to data with length of filter L = 5ns, prediction data with length of filter L = 15ns, prediction range range α = 1ns, and whitening ratio W=5% α = 2ns, and whitening ratio W=1% From the results shown in Figs – 12, we can see that applying the prediction deconvolution filter, interference is much eliminated and the quality of image is much improved In addition, the filter is much Fig Apply the prediction deconvolution filter to data with length of filter L = 10ns, prediction range α = 5ns, and whitening ratio W=1% dependent on channel responses If channel responses are fast, prediction range should be chosen short, otherwise if channel responses is slow, then prediction range should be chosen longer Moreover, deconvolution dependent on for it is GPR prediction seen data that the is mainly range Other parameters are only conditions for us to predict without affecting to processing results The Fig 10 Apply the prediction deconvolution filter to prediction filter is a technique to determine data with length of filter L = 20ns, prediction range channel responses if we can obtain the optimal α = 5ns, and whitening ratio W=1% processing results for arbitrary prediction range Trang 57 Science & Technology Development, Vol 15, No.K1- 2012 CONCLUSIONS filter, Least Square filter, and Weiner filter In the paper, we focus on our proposed prediction deconvolution filter The filter is developed based on some filters such as invert Based on the processed results, we can see that by applying the prediction deconvolution filter, interference is much eliminated and the quality of image is much improved ỨNG DỤNG KỸ THUẬT GIẢI CHẬP DỰ ðỐN CHO XỬ LÝ TÍN HIỆU TRONG HỆ THỐNG RADAR XUYÊN ðẤT Lê Văn Hùng(1), Bùi Hữu Phú(2), Nguyễn Thành Duy(2), Nguyễn Thành Nam(2) (1) ðại Học Công Nghiệp Tp Hồ Chí Minh (2) Phòng thí nghiệm Trọng điểm Quốc gia ðiểu khiển số Kỹ thuật hệ thống, Trường ðHBK TĨM TẮT: Hệ thống radar xun đất truyền lượng song điện từ trường vào lòng đất thu tín hiệu phản xạ trở để xử lý hiển thị hình ảnh vật thể lòng đất Cơng nghệ áp dụng nhiều lĩnh vực khác quốc phòng, xây dựng địa chất Trong báo này, chúng tơi xin đề xuất kỹ thuật giải chập dự đốn cho xử lý tín hiệu hệ thống radar xuyên ñất Kỹ thuật ñược phát triển dựa phương pháp lọc bình phương cực tiểu lọc Wiener Các kết xử lý ñã rằng, với việc áp dụng kỹ thuật giải chập dự đốn, tín hiệu thu loại bỏ can nhiễu cho ảnh tốt với ñộ phân giải cao Hơn nữa, ñể ñạt ñược kết tốt thấy kỹ thuật cần dự đốn xác đáp ứng xung mơi trường truyền Từ Khóa: kỹ thuật giải chập dự đốn, xử lý tín hiệu, radar xun đất REFERENCES [4] Webb D J, Todd L., Ground Penetrating Radar, Steve Cardimona [1] Harry M.J, Ground Penetrating Radar Theory and Applications (2009) [5] Bassem R M, Radar Systems Analysis and Design Using MATLAB (2000) [2] David J D, Ground Penetrating Radar (2004) [6] Dicter G., Metal detector handbook for humanitarian demining (2003) [3] Jeffrey J D, Ground Penetrating Radar Fundamentals (2000) Trang 58 TAÏP CHÍ PHÁT TRIỂN KH&CN, TẬP 15, SỐ K1- 2012 [7] Lieutenant C K K, Detector and Imagery, Proc International Conference personal protective equipment catalogue of Image Processing, 2, 457- 460 (2002) (2009) [11] Faezeh S.A.G., Abrishamian M.S., A [8] Jacqueline M., Alternatives for tank mine detection, RAND (2003) novel method for FDTD numerical GPR imaging of arbitrary shapes based on Fourier [9] Annan A P, GPR—History, Trends, and Future Developments, transform, NDT&E International, 40, 2, 140–146 (2007) Subsurface Sensing Technologies and Applications, 3, ( 2002) [12] Ozdogan Y., Seismic Data Processing, Society of Exploration Geophysicists (2000) [10] Xiaoyin X., Eric L M., Adaptive Difference of Gaussians to Improve [13] www.malags.com Subsurface Object Detection Using GPR Trang 59 ... CONVOLUTION TECHNIQUE Signal processing plays an important part in GPR systems The purpose of the signal processing techniques is to eliminate noise and interference, improve the quality of images,... shape of objects response of environments underground The remaining of the paper is organized as follows In the next section, the model of GPR systems is described The proposed technique of predict... tasks of prediction and deconvolution The characteristics results of processing are much dependent on without dig and destruction The model of GPR the prediction distance The importance of the systems