Identification of Buried Objects in GPR Using Amplitude Modulated Signals Extracted from Multiresolution Monogenic Signal Analysis

It is necessary to detect the target reflections in ground penetrating radar (GPR) images, so that surface metal targets can be identified successfully. In order to accurately locate buried metal objects, a novel method called the Multiresolution Monogenic Signal Analysis (MMSA) system is applied in ground penetrating radar (GPR) images. This process includes four steps. First the image is decomposed by the MMSA to extract the amplitude component of the B-scan image. The amplitude component enhances the target reflection and suppresses the direct wave and reflective wave to a large extent. Then we use the region of interest extraction method to locate the genuine target reflections from spurious reflections by calculating the normalized variance of the amplitude component. To find the apexes of the targets, a Hough transform is used in the restricted area. Finally, we estimate the horizontal and vertical position of the target. In terms of buried object detection, the proposed system exhibits promising performance, as shown in the experimental results.


Introduction
As a geophysical method, ground penetrating radar (GPR) is used in the detection of the targets in near the ground surface areas for locating underground objects such as land mines and pipes. We focus on the metal point detection in this paper. All hyperbolas have to be located and each single radargram has to be analyzed, for the purpose of extracting the exact position of the targets.
There are some researches on buried object detection. To identify hyperbolas, Delbo et al. [1] propose a procedure based on wavelets to reduce noise and then a fuzzy cluster approach to detect objects. Artificial neural networks are used in [2]. A pattern recognition process is used to locate underground objects using a pattern recognition process [3,4]. Real-time interpretation of GPR images is proposed in [5].
A model called Multiresolution Monogenic Signal Analysis (MMSA) has been developed by Unser [6]. Multiple components such as amplitude components and phase are obtained using monogenic signal analysis, which has a proper multiresolution presentation. The wavelet-based amplitude components suppress noise and enhance targets in GPR images. Dong et al. [7] propose synthetic aperture radar (SAR) target classification method based on Riemannian geometry. Combined 1. Extract the amplitude components using the MMSA method; 2. Extract the Region of Interest to narrow down the region to certain areas; 3. Locate hyperbolic patterns via a Hough transformation; 4. Estimate the horizontal and vertical position of the target.
The flowchart is shown in Figure 2. In detail, the GPR image is first decomposed by the monogenic wavelet transform to extract the amplitude component. The amplitude component enhances the target reflection and suppresses the direct wave and reflective wave to a large extent. The phase information decomposed by the monogenic wavelet transform contains too much detailed texture information of all waves and it is hard to locate the target. The method can not only intensify the target, but also eliminate the undesired In detail, the GPR image is first decomposed by the monogenic wavelet transform to extract the amplitude component. The amplitude component enhances the target reflection and suppresses the direct wave and reflective wave to a large extent. The phase information decomposed by the monogenic wavelet transform contains too much detailed texture information of all waves and it is hard to locate the target. The method can not only intensify the target, but also eliminate the undesired presence of the ground surface echo. Then we use the ROI extraction method to restrict the region to a small range. The extraction is based on the normalized variance bigger than a fixed number. The computational cost of the Hough transform is significantly reduced. Then the Hough transformation is used to detect hyperbolic patterns.

Preprocessing Based on the Multiresolution Monogenic Signal Analysis Structure
The MMSA method uses the Riesz-Laplace wavelet transforms. Three wavelet components-amplitude components, phase components and instantaneous frequency components-are extracted. These parameters have a very clear definition in radio frequency theory and they can be extended to two dimensional signals. Using the amplitude component, background clutter is removed to large extent while keeping the target signal.
In this section we first review the monogenic signal. Then, we introduce the Riesz-Laplace wavelet transforms to implement the MMSA method and get the modulation characteristics, which include amplitude, phase and frequency.
Three-components of monogenic signal f pχq are defined in [9] as: where f pχq is a two dimensional signal, χ " px, yq, and is the Riesz transform of f pχq. Amplitude component is defined by: The orientation θ and phase ξ are given by: f " Acosξ, f 1 " Asinξcosθ, f 2 " Asinξsinθ (4) In particular, the amplitude components and phase components are recovered in the direction u " pcosθ, sinθq " p f 1 {r, f 2 {rq , which can be extended to other directions.
Then we show how to realize a monogenic representation of wavelet coefficient. On each bandpass-filtered signal: p f˚ψ i q pxq (5) where ψ i pxq " |detpDq| i{2 ψ`D i x˘is the normalized and spine wavelet. Due to the symmetry characteristics, the coefficients of the signal are defined as: where Riesz coefficient's real component is r 1,i rks and the imaginary component is r 2,i rks. k is the space index and i is the scale index. Based on previous knowledge, the MMSA is applied to extract the amplitude components in the wavelet-domain. The tensor method is used to estimate the local orientation. The corresponding directional Hilbert component is given by: Then the analytic representation is: Then the modulation components are defined by: We use MMSA to define the amplitude component. The frequency component contains too much noise of the reflective wave and it is not so convenient to use this component. In monogenic representation, the local amplitude represents the local energetic information, whereas the phase depicts the local structural information. Thus, the monogenic signal fulfills the invariant property with respect to energy and orientation. Figure 3 illustrates the ability of the MMSA method to extract the amplitude component. With a fixed Gaussian window, we use a tensor-based method to estimate the orientation. Figure 3a is a GPR experiment data profile. It contains recorded point data with a mean frequency of 300 MHz and a time window of 100 ns. The horizontal and vertical coordinates are the trace and sample points, respectively. The number of traces is 540 and the number of sampling points for each trace is 512. Figure 3b illustrates the three amplitude component image extraction result under three level monogenic signal analysis. Three amplitude components are depicted in one picture. As compared with Figure 3a, the ground surface has obvious direct waves, and the first amplitude component suppresses the direct wave and reflective wave to a large extent. This representation not only enhances the target reflection, but also eliminates the redundant echo. Figure 3c shows the enlarged second amplitude-component. The amplitude component makes the target signals obvious. monogenic signal analysis. Three amplitude components are depicted in one picture. As compared with Figure 3a, the ground surface has obvious direct waves, and the first amplitude component suppresses the direct wave and reflective wave to a large extent. This representation not only enhances the target reflection, but also eliminates the redundant echo. Figure 3c shows the enlarged second amplitude-component. The amplitude component makes the target signals obvious.

Extraction the Region of Interest
Cheng proposed the Region of Interest (ROI) extraction method [10]. Based on the analysis of GPR A-Scan signal's statistical features, a windowed statistical method is used to extract the ROI from a large amount of data.
In detail, the variance of the B-scan data is calculated. Then the normalized variance of the data is calculated. We note that the variance is significantly larger in the target area. The ROI is extracted based on the normalized variance being bigger than a fixed number. The first amplitude component extracted by the MMSA is shown in Figure 4a. Then the normalized variance of amplitude component is illustrated in Figure 4b. The extraction of ROI of the amplitude is based on the normalized variance with a lower threshold. The extraction result is shown in Figure 4c. This method gets rid of the false targets and locates the targets accurately and it is especially used for the targets at almost the same depth.

Extraction the Region of Interest
Cheng proposed the Region of Interest (ROI) extraction method [10]. Based on the analysis of GPR A-Scan signal's statistical features, a windowed statistical method is used to extract the ROI from a large amount of data.
In detail, the variance of the B-scan data is calculated. Then the normalized variance of the data is calculated. We note that the variance is significantly larger in the target area. The ROI is extracted based on the normalized variance being bigger than a fixed number. The first amplitude component extracted by the MMSA is shown in Figure 4a. Then the normalized variance of amplitude component is illustrated in Figure 4b. The extraction of ROI of the amplitude is based on the normalized variance with a lower threshold. The extraction result is shown in Figure 4c. This method gets rid of the false targets and locates the targets accurately and it is especially used for the targets at almost the same depth.

Hough Transform
We briefly introduce the Hough transform as follows. We rearrange Equation (1): where   , xt represents the reflection hyperbola's coordinates and 0 x , 0 t , and v are the parameters. We

Hough Transform
We briefly introduce the Hough transform as follows. We rearrange Equation (1): wherepx, tq represents the reflection hyperbola's coordinates and x 0 , t 0 , and v are the parameters. We first limit the image area by the ROI extraction algorithm, so the computational time decreases dramatically. The Hough transform used in our paper was shown in [11]. In our method, ROI limits the area before the Hough transform. In order to reduce noise and artifacts, the image in marked regions is smoothed with Gaussian filters. Then by a canny edge detector, this image is converted into a binary image. Then using the Hough transform, the position of the target is determined. In detail we define the number of accumulator-cells for x 0 and t 0 using the edge pixels. The propagation velocity is an important parameter to obtain the best fitting. It varies for different soil characteristics especially for large range of areas. The velocity v in the Hough transform varies in a given interval assuming the range is not so big, which can be set by the user. Then we transform every edge pixel px, tq and every discrete value of v into the Hough plane with Equation (1). Finally, we draw the location result in the original image (see Figure 5). Firstly, using the Gabor filter, the image in the extracted region is smoothed. By a canny detector, the image becomes a binary image (shown in the middle of Figure 5). Then we use Hough transform in the ROI region. The calculated hyperbolas are drawn in red color.
Sensors 2015, 15 7 varies in a given interval assuming the range is not so big, which can be set by the user. Then we transform every edge pixel   , xt and every discrete value of v into the Hough plane with Equation (1).
Finally, we draw the location result in the original image (see Figure 5). Firstly, using the Gabor filter, the image in the extracted region is smoothed. By a canny detector, the image becomes a binary image (shown in the middle of Figure 5). Then we use Hough transform in the ROI region. The calculated hyperbolas are drawn in red color.

Results
We use GPR numerical simulation images and experimental images to assess the target detection. The electromagnetic simulator "GprMax" is used to generate simulation images using the finite difference time domain (FDTD) method. RIS radar is applied to collect the experimental data.

Simulation Results
The whole simulation process is shown in Figure 6. Figure 6a illustrates a scenario of metal blocks in three distinct steps. This is a simulated image. The width and depth are 2.  Figure 6b which is generated by the "GprMax" simulator. The extraction result of the first amplitude component of the MMSA step is shown in Figure 6c, where the reflection signals and the noise can be suppressed and the target reflection can be enhanced after the extraction of the amplitude component. Then the ROI extraction method is used to get rid of the false

Results
We use GPR numerical simulation images and experimental images to assess the target detection. The electromagnetic simulator "GprMax" is used to generate simulation images using the finite difference time domain (FDTD) method. RIS radar is applied to collect the experimental data.

Simulation Results
The whole simulation process is shown in Figure 6. Figure 6a illustrates a scenario of metal blocks in three distinct steps. This is a simulated image. The width and depth are 2.8 m and 3 m, respectively. The background medium is dry sand and three perfect conductor metal cylinders with 0.01 m diameter are buried at the same depth of 0.45 m. The interval of the three metal targets is 1 m. In the simulation model, the grid in the x and y direction is 0.01 m and detection step is 0.02 m in the x direction. All the boundaries are Perfectly Matched Layers (PMLs). The parameter of the current definition is a Hertzian dipole with unit amplitude and center frequency of a Ricker wavelet of 600 MHz, and the time window for each trace is 25 ns. There are 141 traces in total and 1060 samples. The interval between samples is 2.3587ˆ10´1 1 s. The actual electromagnetic wave velocity is 14.8 cm/ns. The related GPR image is shown in Figure 6b which is generated by the "GprMax" simulator. The extraction result of the first amplitude component of the MMSA step is shown in Figure 6c, where the reflection signals and the noise can be suppressed and the target reflection can be enhanced after the extraction of the amplitude component. Then the ROI extraction method is used to get rid of the false targets and locate the targets accurately. The result is illustrated in Figure 6d. The results allow one to the find the three patterns correctly as can be seen in Figure 6e.  Another result is presented in Figure 7.

Experiment Results
Then we get GPR images in realistic situations. The first example is shown in Figure 8a, which is data from a real GPR experiment. Four metal spheres of 0.02 m diameter were buried under dry sand. These spheres were located side by side. The figure records the detection data with mean frequency of 200 MHz and time window of 80 ns. Finally, the detection result is attached to the picture (see Figure 8b). Further, 0 x and v are estimated by fitting the extracted hyperbola. After the Hough transform, we get that the velocity of the data is v  1.38 × 10 8 m/s, which is tested with the position of the targets in the real situation. As illustrated in Figure 8c, there are four targets in the ground. According to the extracted hyperbolic vertex coordinates, the antenna position of the target is shown in Figure 8c.

Experiment Results
Then we get GPR images in realistic situations. The first example is shown in Figure 8a, which is data from a real GPR experiment. Four metal spheres of 0.02 m diameter were buried under dry sand. These spheres were located side by side. The figure records the detection data with mean frequency of 200 MHz and time window of 80 ns. Finally, the detection result is attached to the picture (see Figure 8b). Further, x 0 and v are estimated by fitting the extracted hyperbola. After the Hough transform, we get that the velocity of the data is v "1.38ˆ10 8 m/s, which is tested with the position of the targets in the real situation. As illustrated in Figure 8c, there are four targets in the ground. According to the extracted hyperbolic vertex coordinates, the antenna position of the target is shown in Figure 8c. For example, the vertex coordinate of the left target is x 1 " 50, so the antenna position of the target is 3 m, which is the same as the position of the target in reality. Besides, the vertex coordinates axis of the hyperbola represents the depth of the target. The vertex coordinate of the left target is t 1 " 97.
A second example provided by the MMSA method is shown in Figure 9. Three similar landmines with a plastic case were buried under dry sand. The mines are Type-72A. The diameter of the landmine is 7.7 cm and the height is 3.7 cm. Figure 9a shows the final detection result with the proposed MMSA method. Note that the proposed detection scheme provides a high detection rate even though the target is not so obvious. Figure 9a is a real GPR data profile. It recorded the point data with a mean frequency of 200 MHz and time window of 50 ns. The detection result is shown in Figure 9b, which illustrates that all patterns are identified with high precision.
The last example is shown in Figure 10, which illustrates the effects of the proposed MMSA detector and the final detection results. Note that the proposed detection scheme provides a high detection rate. Figure 10a is a real GPR data profile. It is recorded landmine detection data with a mean frequency of 200 MHz and time window of 100 ns. This is a two dimensional image. The detection result is illustrated in Figure 10b, which shows that all targets are localized.
Sensors 2015, 15 10 A second example provided by the MMSA method is shown in Figure 9. Three similar landmines with a plastic case were buried under dry sand. The mines are Type-72A. The diameter of the landmine is 7.7 cm and the height is 3.7 cm. Figure 9a shows the final detection result with the proposed MMSA method. Note that the proposed detection scheme provides a high detection rate even though the target is not so obvious. Figure 9a is a real GPR data profile. It recorded the point data with a mean frequency of 200 MHz and time window of 50 ns. The detection result is shown in Figure 9b, which illustrates that all patterns are identified with high precision.
The last example is shown in Figure 10, which illustrates the effects of the proposed MMSA detector and the final detection results. Note that the proposed detection scheme provides a high detection rate. Figure 10a is a real GPR data profile. It is recorded landmine detection data with a mean frequency of 200 MHz and time window of 100 ns. This is a two dimensional image. The detection result is illustrated in Figure 10b, which shows that all targets are localized.  A second example provided by the MMSA method is shown in Figure 9. Three similar landmines with a plastic case were buried under dry sand. The mines are Type-72A. The diameter of the landmine is 7.7 cm and the height is 3.7 cm. Figure 9a shows the final detection result with the proposed MMSA method. Note that the proposed detection scheme provides a high detection rate even though the target is not so obvious. Figure 9a is a real GPR data profile. It recorded the point data with a mean frequency of 200 MHz and time window of 50 ns. The detection result is shown in Figure 9b, which illustrates that all patterns are identified with high precision.
The last example is shown in Figure 10, which illustrates the effects of the proposed MMSA detector and the final detection results. Note that the proposed detection scheme provides a high detection rate. Figure 10a is a real GPR data profile. It is recorded landmine detection data with a mean frequency of 200 MHz and time window of 100 ns. This is a two dimensional image. The detection result is illustrated in Figure 10b, which shows that all targets are localized.  We compare different aspects of the output of K-means+CEM [12], Hyperbolas Automatic Detection algorithm (HADA) [13] with the MMSA method: 1. How many hyperbolas are recognized correctly (true positives) and how many non-hyperbolas/ We compare different aspects of the output of K-means+CEM [12], Hyperbolas Automatic Detection algorithm (HADA) [13] with the MMSA method:
The distance error of all correctly recognized targets.
For the first aspect we investigate three different measurements: Recall " number of true positives number of all actual hyperbolas (13) Precision " number of true positives num. of all hyperbolas(true+false positives) (14) F´measure " 2¨P recision¨Recall Precision`Recal (15) Table 1 show the different results of MMSA, HADA and K-means+CEM. The comparison in Table 1 shows that MMSA improves Precision and Recall as well as the position estimates. These improvements result from the fact that MMSA detects every hyperbola cluster. For K-means+CEM many position estimates have two errors larger than 10 cm, resulting in bad values for "Recall" and "Precision". For correctly recognized targets there is still a distance error of a few centimeters. The reason is that K-means+CEM method has problems with nearby and tangent hyperbolas as well as with background noise. For the HADA algorithm, the values for Recall and Precision are higher than with K-means+CEM, but there are still two position estimate errors larger than 10 cm. MMSA achieves much better results than the other methods with the highest values of Recall and Precision.

Conclusions
In this essay, target detection using MMSA has been demonstrated. This method detects buried objects and estimates their position correctly. The method combines the characteristics of wavelet and energy extraction. The amplitude component of the data is extracted using an unsupervised strategy based on MMSA. After the extraction of the amplitude component of the original date, background noise and direct wave are removed to large extent. We use the ROI extraction method to locate the genuine target area among spurious reflections. Then the labeled area is processed by the Hough transform to search the target's parameters. Finally, we estimate the horizontal and vertical position of the target. Experiments on many different GPR images show that the proposed method provides a general hyperbola-detection system with good results.