Advanced signal processing method for Ground Penetrating Radar. feature detection and enhancement

Transcription

1 Advanced signal processing method for Ground Penetrating Radar feature detection and enhancement Yu Zhang, Anbu Selvam Venkatachalam, Dryver Huston, Tian Xia School of Engineering, University of Vermont, 33 Colchester Ave, Burlington, VT, USA ABSTRACT This paper focuses on new signal processing algorithms customized for an air coupled Ultra-Wideband (UWB) Ground Penetrating Radar (GPR) system targeting highway pavements and bridge deck inspections. The GPR hardware consists of a high-voltage pulse generator, a high speed 8 GSps real time data acquisition unit, and a customized field-programmable gate array (FPGA) control element. In comparison to most existing GPR system with low survey speeds, this system can survey at normal highway speed (60 mph) with a high horizontal resolution of up to 10 scans per centimeter. Due to the complexity and uncertainty of subsurface media, the GPR signal processing is important but challenging. In this GPR system, an adaptive GPR signal processing algorithm using Curvelet Transform, 2D high pass filtering and exponential scaling is proposed to alleviate noise and clutter while the subsurface features are preserved and enhanced. First, Curvelet Transform is used to remove the environmental and systematic noises while maintain the range resolution of the B-Scan image. Then, mathematical models for cylinder-shaped object and clutter are built. A two-dimension (2D) filter based on these models removes clutter and enhances the hyperbola feature in a B-Scan image. Finally, an exponential scaling method is applied to compensate the signal attenuation in subsurface materials and to improve the desired signal feature. For performance test and validation, rebar detection experiments and subsurface feature inspection in laboratory and field configurations are performed. Keywords: Ground Penetrating Radar, Curvelet Transform, Clutter Removal, Rebar Detection 1. INTRODUCTION Ground penetrating radar (GPR) is a rapidly growing field over the past years as a noninvasive detection technique. It utilizes electromagnetic waves to study the underground structures and detect the subsurface objects. As a main structural component, the buried rebar plays a significant role in supporting highway or bridge deck reinforced concrete. Thus, it is important to identify rebar location and condition. A variety of GPRs are currently available for rebar detection[1], [2]. During the inspection, the radar transmitter emits EM waves into the subsurface structure and a receiver collects the reflected signal. By analyzing this reflected signal, the properties of the underground structure can be characterized and the subsurface object can be localized. During GPR surveys, environmental noise, systematic noise and other radio frequency interference signals can blur the desired GPR signal. Meanwhile, clutter, such as a strong reflection from an air-ground surface and antenna direct coupling, can mask the signature signals of the subsurface structure. There is a considerable amount of research literature on GPR signal processing. The GPR signal enhancement methods for landmine detection have been studied for many

2 years and many effective algorithms have been proposed[3], [4]. However, when it comes to rebar detection, the smaller reflecting cross sections lead to lower amplitude reflection signals. Therefore, the signal features in the raw radar data are weaker, which requires more sophisticated signal enhancement method. The recorded radar response at a specific position is an A-Scan waveform, which is a measure of the reflected signal amplitude with respect to time. B-Scan image is obtained by combining all A-Scan waveforms along the radar antenna moving direction. In a B-scan image, the vertical axis is EM wave transmission time (or penetrating depth) and the horizontal axis is the GPR spatial location. A buried rebar appears as a hyperbola in the B-Scan image. The three major factors that impair the rebar feature are: (1) Environmental and systematic noises can blur the hyperbola; (2) Strong Clutter can conceal the hyperbola; (3) Power loss due to subsurface material absorption can attenuate reflection signal amplitude. A good GPR signal processing method therefore should consider all three factors while preserving the rebar feature in B-Scan image. Several radar signal methods have been investigated to improve the quality of B-Scan image, but none of them can address all these three issues concurrently. Short Time Fourier Transform (STFT) is used to perform joint time and frequency characterization in some articles[5]. However, the STFT is just an analysis tool focusing on A-Scan waveform, and the denoising process is accomplished by a follow-up band pass filter based on non-adaptive cut-off frequency. For different GPR data set, different cut off frequency need to be determined by human decision, which is a non-adaptive procedure. Meanwhile, since STFT deals with GPR data trace by trace, it does not take the relation between each trace (A-Scan waveform) into account or consider the B-Scan image as an entire 2D image. This leads that processing based on STFT analysis result will change the shape of hyperbola in B-Scan image. Another method used Wavelet Transform (WT) to decompose and reconstruct the GPR signal[6]. WT provides almost optimal representation of a 1D signal, but for a 2D signal (image), the standard WT based de-noising methods have been recognized as incompetent to extract the object features[7]. Another widely used method to remove noises and ground reflection is average (or background) removal, which calculates the average of the first several A-Scan waveforms as the background and then subtracts this average value from the B-Scan image[8]. The limitation of average removal is that the materials of the background in B-Scan image should be homogenous and the air-ground surface should be totally flat. Independent Principal Component Analysis (IPCA) is also a conventional clutter removal method. IPCA uses the mathematical modeling principle to decompose the signal into different components, and then finds out the components corresponding to object and clutter respectively[9]. This method works well for clutter removal, but it is hard to distinguish object and clutter automatically. A set of GPR signal enhancement algorithms that can remove noises and clutter while preserving and enhancing the rebar features in a B-Scan image is proposed in this paper. In Section 2, the principles of the three steps of the processing algorithm are explained respectively. Section 3 briefly describes the data acquisition using our developed GPR system. Several rebar experiments are conducted. The test results are compared with existing GPR signal processing method to verify the competence of the proposed algorithm in Section 4.

3 2. METHODOLOGY 2.1 Algorithm structure GPR Raw Data Denoising Cluter Removal Amplitude Scaling Enhanced GPR Data Figure 1 Algorithm structure Our proposed GPR signal enhancement algorithm contains three steps as shown in Figure 1. The input of this algorithm is GPR raw data, and then Curvelet Transform is applied to remove the environmental and systematic noise. In the second step, a 2D high pass filter (HPF) removes the clutter (ground reflection). Before building the filter, 2D frequency characteristics of object reflection signal and clutter are analyzed respectively, and then cutoff frequency for the 2D HPF is determined based on the frequency analysis result. Upon completing these two steps, noise and clutter are removed and the hyperbola feature stands out. A result of GPR signal attenuation during transmission is that the amplitude of rebar reflection signal can be very weak, which results in insignificant hyperbola in the B-Scan image. To compensate for the signal loss, an amplitude scaling procedure is applied to scale up rebar reflection signal based on the analysis of signal attenuation factor in media. 2.2 Radar signal de-noising The Curvelet transform (CT) is a multi-scale analysis algorithm[7] that is more suitable for image de-noising than the wavelet transform (WT), since it can better analyze the line and curve edge characteristics, and it has a better approximation precision and good directivity. The CT of a function is [ 10] c(j, l, k) = f, φ j,l,k (1) where φ j,l,k is the curvelet and j, l, k = (k 1, k 2 ) are the parameters of the scale, the direction and the position respectively. The curvelet mother function is defined in the Fourier domain by φ j(r, θ) = 2 3j 4 W(2 j r)v( 2[j/2] θ 2π ) (2) where polar coordinates (r, θ) is used in Fourier domain. W and V are the radial window and angular window respectively. These two functions are smooth, non-negative and real-valued, with W taking positive real arguments. W and V restricts φ j to a polar wedge that is symmetric respect to zero. Then the family of curvelets φ j,l,k is defined at scale 2 j, direction θ l and position x (j,l) k = R 1 θl (2 j k 1, 2 j/2 k 2 ) as where R θ is the rotation matrix for θ radians defined as φ j,l,k = φ j (R θl (x x k (j,l) )) (3) cos θ sin θ R θ = ( sin θ cos θ ) (4) 1 R θ is its inverse. The curvelet transform of a function is expressed as the following convolution c(j, l, k) = f, φ j,l,k = R 2f(x)φ dx j,l,k (5) Figure 2 illustrates the window for Curvelet Transform, which consists of rectangular windows and angle windows.

4 The rectangular window provides the multi-scale characteristic and the angle window provides direction characteristic. The direction division is realized by rotation and translation on the angle window function. Through Curvelet Transform, the object signal which has large scale and direction can be distinguished from the noise which has small scale and non-direction. Figure 2 Curvelet Transform window To determine the threshold between the curvelet coefficients of object signal and noise, some calculations have been done by Starck, J. L. [ 11]. The noisy data are modeled as x i,j = f(i, j) + σz i,j (6) where f(i, j) is original image, z i,j is white noise, and σ is the standard deviation of noise. The threshold of the curvelet coefficients C j,l for each position can be determined as following procedure [ 12]. σ can be calculated using Bayes Shrink method as σ = median( C j,l ) (7) where C j,l are the curvelet sub-band coefficients at a certain position of the input image with noise. The variance of a noisy image can be calculated by σ c 2 = 1 The standard variance of the original image is obtained as Finally, the adaptive threshold of the curvelet coefficients is And the filtered curvelet coefficients C j,l for each position can be determined by C MN j,l l,j 2 (8) σ f = σ c 2 σ 2 (9) T = σ2 σ f (10) C j,l = { C j,l, if C j,l T 0, if C j,l < T The flow chart of CT denoising processing is shown in Figure 3. The Curvelet Transform coefficients φ j,l,k of B-Scan image is calculated first by (2)-(5), and then equation (7)-(11) are applied to determine the new curvelet coefficients φ j,l,k. Finally, after applying the inverse curvelet transform to φ j,l,k, the processed B-Scan image is obtained. Both of CT and inverse CT are implemented by Fast Discrete Curvelet Transform (FDCT) via Frequency Wrapping [ 13]. (11)

5 Raw B-Scan Fast Discrete Curvelet Transform Thresholding Curvelet Coefficients Inverse Fast Discrete Curvelet Transform Denoised B-Scan Figure 3 Flow chart for de-noising 2.3 Clutter removal The reflection signal from the air-ground surface displayed as horizontal white and black strips in B-Scan image is clutter. Comparing with object reflection signal, amplitude of clutter is so strong that it blurs the object feature in B-Scan image. To remove the clutter, models of clutter and rebar are developed and the associated frequency characteristics are investigated. Based on these analysis, a cutoff frequency is determined and a 2D high pass filter (HPF) is built to remove the clutter while preserve the hyperbola in B-Scan image Clutter model The ideal noiseless clutter has been modeled for continuous GPR signal and the spectrum interval of its principal energy has been calculated through frequency analysis by Potin, D. [ 14]. For discrete GPR raw data, the clutter can be modeled as f c [m, n] = { A, 1 m M, N 1 n N 2 0, elsewhere where M is the number of traces in B-Scan image, N 1 is the first point of clutter, and N 2 is the last point of clutter. m and n are indices of the sample in x and y direction. The magnitude spectrum of f c [m, n] is (12) F c (u, v) = A 1 e j2πumx 0 1 e j2πux 0 1 e j2πv(n2 N1+1)y0, u 0, v 0 1 e j2πvy 0 AM 1 e j2πv(n 2 N1+1)y0, u = 0, v 0 1 e j2πvy 0 A(N 2 N 1 + 1) 1 e j2πumx 0, 1 e j2πux 0 u 0, v = 0 { AM(N 2 N 1 + 1), u = 0, v = 0 (13) where x 0 and y 0 are spatial intervals between consecutive signal samples in x and y directions. In an analogy with the continuous GPR signal, the main energy F c (u, v) of the discrete GPR signal locates in the

6 first two lobes of its magnitude spectrum. Thus the energy of clutter band mostly locates in the subspace Rebar model E c = {(u, v) u 2 2, v = } (14) Mx 0 (N 2 N 1 +1)y 0 Figure 4 Rebar model A mathematical model for object in B-Scan image has also been introduced by Potin, D. [ 14]. Using the same sample intervals as in the clutter model. The rebar model is built as Figure 4. Assuming the depth of the object is z 0, the radar signal transmission time in air is t 0 and the transmission velocity is v, the discrete model for ideal hyperbola without noises in B-Scan image can be derived as f r [m, n] = { δ [n n 0 a (m m 0 )2 + 1], if m m b 2 0 m 0, elsewhere (15) where 2z 0 vy 0 = a, z 0 x 0 = b and m is the half width of the hyperbola. The magnitude spectrum of f r [m, n] is 1 e j2πu(2 m+1)x0, u 0 F r (u, v) = { 1 e j2πux 0 2 m + 1, u = 0 (16) Correspondingly, the main energy of F r (u, v) locates in the first two lobes of its magnitude spectrum. So the energy of rebar hyperbola mostly locates in the subspace High pass filter E r = {(u, v) u 2 (2 m+1)x 0, v} (17) Comparing E c in clutter model and E r in the rebar model, for any v, the sampling number of the B-Scan image is much larger than that of hyperbola, leading so the following relation 2 Mx 0 2 (2 m+1)x 0 (18) Formula (18) specifies that the bandwidth of the main energy of clutter is much narrower than that of rebar in x direction. When v = 0, the normalized magnitude spectrum of clutter and rebar reflection signal appears in Figure 5. In this figure, M = 1000, m = 50 and x 0 = , so that the energy of clutter mainly locates in [ ] and the rebar

7 energy mainly locates in [ ]. Figure 5 Normalized magnitude spectrum of clutter and rebar for v = 0 Based on the formula (18), a two dimension high pass filter (HPF) can be applied to remove the energy of clutter while protecting most of the energy of the rebar. The cutoff frequency of this HPF is 2.4 Amplitude scaling u cutoff = 2 Mx { 0 2 (19) v cutoff = (N 2 N 1 +1)y 0 To eliminate the signal attenuation during transmitting in concrete and enhance the rebar reflection signal, a scaling parameter A(d) is multiplied to the amplitude of received signal at different depth. A deeper d corresponds to a larger the A(d). To construct the amplitude scaling function A(d), the attenuation coefficient in concrete should be determined. The gain function of signal transmitted in some material is [ 15] g(n) = g(1) + g(n) g(1) (n 1) (20) N 1 where n (n = 1, 2,, N, and N is the total samples number) represents the index of the sample along the y direction in the B-Scan image (time axis). So the gain of GPR signal in concrete in db has a linear relation with the penetrating depth. Assuming the signal amplitude in mv at the ground surface is V(0) and the signal amplitude at the depth d is V(d), the relationship can be expressed as 20 log ( V(0) ) = αd (21) V(d) where α is the attenuation coefficient with the units db/inch. From equation (21), the formula for V(d) can be derived V(d) = V(0) 10 αd 20 (22) which means that the relationship between V(0) and V(d) is close to exponential. In equation (22), the value of α can be determined by [ 15] α = ω εμ { 1 2 [ 1 + ( σ ωε )2 1]} with σ is the electrical conductivity, μ = μ 0 = 4π 10 7 henry/m, ω = 2πf, f is the frequency in Hz, ε = 1 2 (23)

8 Relative Dielectric Permittivity ε 0, and ε 0 = F/m is the dielectric permittivity of the vacuum space. When the penetrating depths increase by d inches, the transmitting distances increase by 2d inches. Then if the signal attenuation vs. transmitting distance in concrete is α with unit db/inch, the signal attenuation coefficient vs. penetrating depth is 2α with unit db/inch. So an exponential parameter A(d) can be multiplied by V(d) to revert its amplitude to the same level with V(0). And the scaling function A(d) is derived base on equation (22) where d is the distance between rebar and air-ground surface. A(d) = 10 2αd 20 = 10 αd 10 (24) 3. DATA ACQUISITION Figure 6 High speed UWB GPR system In this paper, the GPR data is collected by our developed high speed UWB GPR system [ 16]. As shown in Figure 6 High speed UWB GPR system, this GPR system consists of five important functional units: (1) RF transmitter; (2) Ultra-wideband antennas; (3) Data acquisition comprising the high speed real time digitizer, high speed data transmission and storage unit; (4) Multi-core computer and (5) FPGA digital controller along with a wheel encoder. The RF transmitter comprises of a UWB pulse generator [ 17] that generates high amplitude Gaussian pulses (18 V peak-to-peak) with a wide range of pulse repetition frequency (PRF) determined by the FPGA. The UWB antenna used in this GPR system is a novel Good Impedance Match Antenna (GIMA) [ 16] [17][18] whose return loss is less than -10 db from 500 MHz to 6 GHz which attests high-quality impedance matching across the wide frequency band for effective signal transmission and reception. The high speed digitizer comprises of a 10-bit, 8 GHz real-time sampling ADC and high throughput data transmission unit connected to the computer via PCIe connection. The computer streams the data from the digitizer, tags the data with header details. An optical encoder measures the scan distance via quadrature pulses generated based on distance travelled. The FPGA receives the pulses from the wheel encoder to perform travel distance trigged scans. The distance information and time stamp are transmitted to the computer for creating the data headers. 4. EXPERIMENTS AND RESULTS 4.1 Experiments in lab To verify our proposed GPR signal enhancement algorithm, each steps of this algorithm is tested in lab using several rebar configurations.

9 4.1.1 Curvelet Transform de-noising test A raw GPR data is processed using Curvelet Transform to remove the environmental and systematic noise. Figure 7(a) and (b) are the raw GPR data and GPR data after denoising respectively. Compared with raw A-Scan waveform, the denoised A-Scan waveform is much smoother in Figure 7(b). Figure 8 shows the processing result using different denoising methods for the same B-Scan image. As shown in Figure 8(b) and Figure 8(c), using low pass filter and Curvelet Transform denoising achieve good de-noising performance. However, the hyperbola polluted by noise is better recovered when CT denoising is applied since Curvelet Transform can effectively deal with the line singularities in a 2D signal. So Curvelet Transform denoising can effectively remove noises in B-Scan image as well as preserve the shape of rebar hyperbola. Figure 7 Performance of Curvelet Transform de-noising Figure 8 Comparison of low pass filter and Curvelet Transform D filter clutter removal test Various rebar configurations are built to test the performance of the second step, 2D Filter Clutter Removal in our proposed algorithm. Three rebar test configurations are conducted: one rebar on floor, two rebars on floor with same height and two rebars on floor with different heights. Figure 9(g) shows the test setup for two rebars on the floor with

10 different heights. The raw B-Scan images for each setup are displayed as the first row of Figure 9, while the clutter removed B-Scan image for each setups are shown as the second row of Figure 9. For all these three rebar configurations, our proposed 2D filter can remove the air-ground surface reflection while protest the rebar reflection signal. Figure 9 Performance of clutter removal: (a) Raw B-Scan image of one rebar; (b) Clutter removed B-Scan image of one rebar; (c) Raw B-Scan image of two rebar with same height; (d) Clutter removed B-Scan image of two rebar with same height; (e) Raw B-Scan image of two rebar with different heights; (f) Clutter removed B-Scan image of two rebar with different heights; (g) Test setup for two rebar on the floor with different heights. For further validation, the comparison between the performances of our 2D filter and Average Removal method[8]error! Reference source not found. is performed using other three rebar configurations shown as Figure 10: (a) One rebar is buried in a sandbox placed on the floor; (b) One rebar is buried in a sandbox, and another rebar is placed on the floor beside the sandbox; (c) A concrete slab containing two rebar is placed on the floor, and the distance between these two rebar is 8 inches. Figure 10 Rebar test configurations: (a) One rebar in the sandbox; (b) One rebar in the sandbox and another rebar on the floor; (c) & (d) Two rebar in the concrete slab. As shown in Figure 11, for the one rebar in sandbox configuration, Average Removal cannot remove the clutter caused by the reflection signal from the top and bottom surfaces of sandbox, while our 2D filter can remove all these clutters. As shown in Figure 12, for the one rebar in sandbox and one rebar on floor setup, Average Removal cannot remove ground reflection completely. The hyperbola is still masked by clutter, while the 2D filtering can make both two rebars visualizable. These two results indicates when the background materials are not homogeneous, i.e. containing air,

11 soil, sand and concrete, the Average Removal cannot effectively remove all the clutter, while 2D filter can eliminate all kinds of these clutters. Figure 11 Comparison of 2D filter and average removal (one rebar in sandbox): (a) Raw B-scan image; (b) Average removal result; (c) Clutter removal result using 2D filter Figure 12 Comparison of 2D filter and average removal (one rebar in sandbox and one rebar on floor) : (a) Raw B-scan image; (b) Average removal result; (c) Clutter removal result using 2D filter Figure 13 Comparison of 2D filter and average removal (two rebars in concrete slab): (a) Raw B-scan image; (b) Average removal result; (c) Clutter removal result using 2D filter In the two rebar in concrete slab configuration, as shown in Figure 13, the two hyperbolas overlap as one plane in raw B-Scan image. When applying Average Removal, the image equality is not improved significantly and a new clutter (concrete-ground surface reflection) is brought into B-Scan image. When applying 2D filter, all clutters are removed and two hyperbolas are separated. This result verifies, when the distance between two rebars is small, 2D filter has a much better performance than Average Removal Amplitude scaling The image quality of B-Scan image before and after amplitude scaling is compared to verify the validity of the third step in our GPR signal enhancement algorithm. In this test, the value of α in amplitude scaling function (24) is

12 determined as 2dB/inch using equation (23). As shown in Figure 14(a), the bright strip at the top of the raw B-Scan image is the strong ground surface reflection. Comparing to the high magnitude of this clutter, the gray scale of hyperbola pixels is so weak that it is hard to distinguish the rebar and background. As shown in Figure 14(b), the signal attenuation factor is eliminated and the hyperbola becomes prominent after amplitude scaling in the processed B-Scan image. The third step of our algorithm can approach the expected target. Figure 14 Performance of amplitude scaling: (a) Raw B-scan image; (b) Scaled B-scan image 4.2 Real test outdoor A real outdoor road experiment is done to test performance of the whole GPR signal enhancement algorithm. In this experiment, the test configuration is shown as Figure 15(a): (1) one rebar is buried 1 foot deep underground; (2) the diameter of this rebar is 1.5 cm; (3) Underground materials are soil and stone pebbles; (4) GPR antennas are 14 inches above ground surface. As shown in Figure 15(b), the raw B-Scan image is blurred by noise and rebar hyperbola is weaken by clutters (air-ground surface reflection and direct coupling signal). In the first step, environmental and systematic noises are removed. As shown in Figure 15(c), the resulted B-Scan image is smoother than the raw image. In the second step, clutters are removed and hyperbola feature stands out. As shown in Figure 15(d), 2D filter can eliminate the direct coupling completely. Since the air-ground surface is not flat, some residual clutter exists after processing. However, the intensity of these resides are not as strong as that in Figure 15(c), so the hyperbola feature is still enhanced. In the last step, the effect of signal attenuation during transmission is removed. Here, according to equation (23), parameter α in amplitude scaling function is approximated as 2dB/inch. As shown as Figure 15(e), the hyperbola becomes more prominent after the amplitude scaling processing. The output B-Scan image quality is improved. Figure 15 One rebar buried 1 foot underground test: (a) Outdoor test scenery; (b) Raw B-scan image; (c) De-noised B-scan image; (d) Clutter removed B-scan image; (e) Scaled B-scan image

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