Abstract
An image domain CLEAN technique, for nondestructive and noncontacting subsurface imaging, is discussed. Recently introduced finite-difference time-domain- (FDTD-) based virtual tool, GrGPR, is used to create imaging scenarios and to generate synthetic scattering data through synthetic aperture (SAR) type scanning. Matlab-based imaging algorithms are used to process recorded FDTD data. The location and the geometry of the targets are obtained by image domain CLEAN technique which is extracting scattering centers from the SAR image. The effectiveness of the algorithm is tested in simulated data.
1. Introduction
Imaging and detection are two keywords in searching/diagnosing tumors, buried land mines, people under debris, and so forth [1–9]. The first essential step in these tasks is subsurface imaging (SSI) which is based on illuminating an area/object with a sensor (or a group of sensors) and processing forward and/or backward scattered signal. The sensor technologies as well as computer algorithms are in a quite mature stage to accomplish these tasks. The imaging information is hidden in the difference of electromagnetic (EM) parameters (e.g., permittivity) in the environment, and identification of something within this subsurface image is an extremely difficult task which necessitates the use of intelligent detection and identification methods, adaptive noise, and clutter elimination approaches. Most of imaging algorithms rely on linear procedure to comply quick imaging requirement. Inverse scattering is a widely used imaging algorithm which is based on the reconstruction of electromagnetic properties of unknown scatterers by inverting scattered field measurements [10]. Inversion procedures are usually quite complex and time consuming, especially when high-resolution images are needed. In the literature, some deterministic and stochastic approaches have been proposed for solving this problem. Stochastic approaches are global optimization methods and are usually based on population-based solutions such as genetic algorithm, ant colony optimization, and particle swarm optimization, which are optimization methods used in electromagnetics for image reconstruction [10–17]. It is still a quite difficult task to develop effective reconstruction procedures, and better algorithms are still required. Tests should be performed with data, recorded or synthetically generated under scenarios as realistic as possible.
Data acquisition within such realistic experiments is very expensive and time consuming and sometimes could be dangerous as well. Therefore, numerical models are very attractive. Numerical models have gained high importance in electromagnetics (EM). Instead of using expensive and time consuming experimental setups, numerical modeling of complex electromagnetic problems is highly preferred. There are many powerful time and frequency domain methods in EM. The most famous one is the finite-difference time-domain (FDTD) method [18]. The FDTD method is easy to understand and implement and has been widely used in subsurface numerical modeling [19, 20]. With the aid of visualization, FDTD has become very powerful in EM not only for research but also for engineering education purposes. Considering the advantages and importance of easy-to-use design steps, a set of FDTD-based virtual tools has been introduced to the use of engineering society [21–28].
In this study, SSI is discussed in 2D simplified environments. The first part of the study is focused on synthetic data acquisition. Recently introduced, 2D FDTD-based virtual EM tool, GrGPR, is used to create various SSI scenarios and to generate synthetic scattering data through synthetic aperture (SAR) type scanning. Matlab-based algorithms are used to process recorded FDTD data in order to construct the images of the objects [28]. In addition to the prior, in this study, CLEAN technique-based feature extraction method is applied to obtain the structural frame of the objects. The CLEAN technique is based on extracting scattering centers [29–31], and in this study the images obtained via this method are referred to as scattering centers.
2. SSI: Image Reconstruction Algorithm
In this study, GrGPR virtual tool is used in generating synthetic data for various shaped objects. The images that will be processed with CLEAN algorithm are priorly created by MATLAB-based imaging algorithms. GrGPR is used to record raw FDTD data.
GrGPR gives us the opportunity to create and locate triangular, rectangular, and/or elliptical objects, either perfect electrical conductor (PEC) or lossy, by just selecting an object and clicking/dragging the mouse (Figure 1). A flat or irregular lossy ground with buried objects may be generated. The irregular terrain is produced automatically using cubic-spline interpolation algorithm once the user locates a number of points and fills the area between the curve and the bottom (left mouse button) or top (right mouse button) boundary [27].
(here, is set to 50) radiators/receivers are located in pair. Gaussian pulse excitation is selected from the other signal types (i.e., continuous wave, rectangular pulse, and linear FM). The antenna pairs are activated sequentially for SAR type scanning. Then the raw signal which contains both early- and late-time responses is recorded by GrGPR receiver.
Early-time response, which consists of the transmit signal and the signal reflected from the boundary/skin layer, is obtained by repeating the GrGPR simulations without the object under investigation. Information related to the scattering object is hidden somewhere in the late-time response and can be achieved by subtracting the early-time response accordingly.
The accumulation of late-time responses from every single cell to a pair of radiator/receiver necessitates the calculation of round-trip signal delay. Denote coordinates of each cell/pixel by (), where and are the horizontal and vertical axes, respectively. Coordinates of the th radiator/receiver pair are denoted by . The time necessary for a round trip from the radiator to the cell/pixel and back to the receiver can then be calculated via where is the speed of light. The corresponding pixel (distance) index is directly obtained from where is the FDTD time step. The field intensity of each cell (i.e., the image color) is then formed as where is the intensity at . Note that round-trip delays calculated from (1) must be replaced by an expression which takes into account Snell’s law if an object buried under the lossy ground is of interest. In summary, the three-step SSI algorithm is based on the calculation of the time delays of all round trips from all pixels to all scan points, noise/clutter elimination and signal enhancement (i.e., matched filtration), and superposing scattered field values corresponding to those delays.
Since the aim of this study is to examine the applicability of the CLEAN technique, the objects under investigation are assumed to be in free space and the elimination of surface effect is neglected; so the study is focused on improving the imaging quality.
3. CLEAN Algorithm
CLEAN algorithm is one of the challenging signal processing techniques for microwave imaging, which was originally developed for astronomy in 1974 [29] and adopted for microwave imaging applications since 1988 [30].
In the literature, CLEAN technique is applied for two types of image processing: one is to get rid of the clutters in the image to enhance the image quality and the other is used to determine the scattering centers of the image. The image quality enhancement is achieved by subtracting the residual image data from the original one. However, this study is focused on scattering centers method, and a sample scenario is given for the other latter.
The intensity of two-dimensional scattering centers is subtracted one at a time from the priorly formed SAR image equation (3) using image domain CLEAN technique. The scattering centers are iteratively identified after each subtraction step and then removed from the progressive residual of the image, proceeding from the strongest to weakest stronger scattering center (4). This process allows for each scattering center to be more accurately distinctive in the absence of the prior. All scattering centers for a target are identified when the residual reaches a priorly identified threshold (). Lastly, these 2D scattering centers are placed in a multidimensional grid of 2D space () according to their spatial behavior (5). Consider It must be noted that each subtraction is performed not only for a single scattering point but within predetermined neighbourhood to increase the speed of the algorithm. The center scattering point is assumed to be the strongest one within this neighbourhood and selected as the scattering center. The flowchart of the applied image domain CLEAN algorithm is given in Figure 2.
The residual data is assumed to be belonging to the clutter. When the residual data is removed from the starting image data , the resultant is the CLEANed image that is given in
4. Sample Scenarios and Canonical Examples
Various SSI scenarios are created using the GrGPR tool, and scattered time data are recorded; then images are reconstructed via the SSI algorithm developed. All examples presented here are run for a Gaussian UWB pulse. The transmit/receive antenna pair is located at 50 different points around the object under investigation on a circular path and activated sequentially to perform a contour-SAR scan. All objects presented below are PEC. The images are formed by two different algorithms: SAR processing and image domain CLEAN technique which is called scattering centers in this study.
To prove the correctness of the applied method, a simple square PEC object is located in free space and the 50 transmit/receive antenna pairs are placed around this object (Figure 3). The original image of the object is pictured on the left. The images obtained by SAR processing and scattering center are given in the middle and on the right, respectively. The total elapsed time to reconstruct both images is 14 seconds.
In Figure 4, the examples of two PEC objects with different geometries are given. The original images of the objects (Figure 4(a)) are compared with the images obtained via SAR processing (Figure 4(b)) and scattering center (Figure 4(c)), respectively. The scattering center images are obtained for both Gauss (stars) and Linear FM-Chirp signals (diamond). The total elapsed time to reconstruct the images of each geometry is 20.4 (top) and 20.6 (bottom) seconds.
(a)
(b)
(c)
In Figure 5, a more complex object (Figure 5(a)) is preferred and the images are given for both SAR processing (Figure 5(b)) and scattering center (Figure 5(c)). The consistency of the images can be observed. The scattering corners and edges can be detected in spite of the complexity of the object. The total elapsed time to reconstruct both images is 19 seconds.
A sample for image quality enhancement is given in Figure 6. The original image is pictured in Figure 6(a). As in previous example the SAR-processed and scattering center images are obtained (Figures 6(b) and 6(c), resp.). Then the CLEANed image is reconstructed by subtracting residual image data, from the original image data, and this is pictured in Figure 6(d). It can be observed that the clutter effects due to scattering are mostly removed in the last image. The time elapsed for the SAR image, scattering centers, and the CLEANed image is 30 seconds.
5. Conclusion
A CLEAN technique-based feature extraction method, which is, in this study, referred to as scattering center, is discussed. A FDTD-based GrGPR virtual tool is used to generate forward scattered data synthetically. The tests are done for PEC objects with various shapes. The images, obtained with two different methods, are compared, and the consistency of the results is shown. The CLEAN technique can be used for two different approaches: image enhancement and feature extraction. The tests for image enhancement show that the clutter effects can mostly be reduced via this method. And the contour of the even complex images can be obtained by the feature extraction capability of the algorithm. The CLEAN technique can be used for two different purposes, and this strengthens the method.