Application of Support Vector Machines for Estimating Wall Parameters in Through-Wall Radar Imaging

Hindawi Publishing Corporation International Journal of Antennas and Propagation Volume 2015, Article ID 456123, 8 pages http://dx.doi.org/10.1155/2015/456123 Research Article Application of Support Vector Machines for Estimating Wall Parameters in Through-Wall Radar Imaging Hua-Mei Zhang,1 Ye-Rong Zhang,1 Fang-Fang Wang,1 and Jun-Lin An2 1 School of Electronic Science and Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, China Institute of Atmospheric Physics, Nanjing University of Information Science & Technology, Nanjing 210044, China 2 Correspondence should be addressed to Hua-Mei Zhang; Received 27 November 2014; Accepted 25 April 2015 Academic Editor: Jaume Anguera Copyright © 2015 Hua-Mei Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In through-wall radar imaging (TWRI), ambiguities in wall characteristics including the thickness and the relative permittivity will distort the image and shift the imaged target position. To quickly and accurately estimate the wall parameters, an approach based on a support vector machine (SVM) is proposed. In TWRI problem, the nonlinearity is embodied in the relationship between backscatter data and the wall parameters, which can be obtained through the SVM training process. Measurement results reveal that once the training phase is completed, the technique only needs no more than one second to estimate wall parameters with acceptable errors. Then through-wall images are reconstructed using a back-projection (BP) algorithm by a finite-difference time-domain (FDTD) simulation. Noiseless and noisy measurements are discussed; the simulation results demonstrate that noisy contamination has little influence on the imaging quality. Furthermore, the feasibility and the validity are tested by a more realistic situation. The results show that high-quality and focused images are obtained regardless of the errors in the wall parameter estimates. 1. Introduction Though-wall radar imaging (TWRI) is a form of nondestructive detection that has applications in civil engineering and security. In TWRI, if the wall parameters such as the wall thickness and the relative permittivity are known in advance, the changes in the speed and the amplitude attenuation of the electromagnetic waves that pass through the wall can be calculated accurately. Moreover, the refraction point of the electromagnetic waves can be determined precisely. Hence, targets behind walls can be easily detected and located. There have been many studies on TWRI that have created highquality images with known wall parameters [1–3]. However, wall parameters are generally not known a priori. If the wall parameters are not properly considered, the TWRI images will be fuzzy or distorted and the positions of the targets in the image will be incorrect. Walls are commonly constructed with brick, wood, glass, plaster, or concrete block, and the propagation of EM waves in these materials differs. Efforts have been made to understand the effects of various common building materials. In addition, efforts have been made to image or locate the target through building walls with unknown characteristics [4–7]. Although these methods can provide high-quality, that is, focused, images, certain algorithms rely on knowledge of the wall parameters such as the dielectric constant, the wall thickness, and the conductivity. In recent years, various studies have attempted to estimate the values of wall parameters. At several different transceiverreceiver separations various time-delay-only measurements were proposed for a wall parameter estimation. The estimated wall parameters can be utilized for improving the accuracy of real-time locating and tracking of moving humans [8, 9]. Through setting various targets located at various distances on the other side of the wall, the frequency domain data was converted to time domain and then mapped with spatial domain to estimate the wall parameters. But this technique can only be experimented in a known environment [10]. Multichannel radar antennas were used to accurately and simultaneously estimate both the wall parameters and the target position [11]. A linear trajectory was fitted to a set of target images assuming various wall thicknesses via the 2 Radon transform for each assumed dielectric constant [12]. The intersection of the trajectories corresponding to the various dielectric constants was taken as the estimated target position, which was then used to obtain estimates of the wall thickness and the dielectric constant. All above methods require the use of two or more antenna arrays or at least two measurements. Measurement methods are effective in a lab, but their usefulness is limited in practice. Other methods construct a cost function between wall parameters and a computer index, such as the sharpness of the target images and the entropy [13, 14]. These methods attempt to minimize the cost function and can produce satisfactory images, but they impose a significant computational burden. The estimation of wall parameters was approached as a least squares problem based on a forward model of electromagnetic wave propagation in a homogeneous wall [15]. Two filter-based approaches were developed and can provide quick and precise estimates of wall parameters, but they do not work well in low-SNR conditions. In this study, we use a novel approach to obtain quick and precise estimates of wall parameters. The approach is based on SVMs. The SVM, which was introduced by Vapnik, is a statistical learning method. The SVM is based on the VC dimension and structural risk minimization. By solving a convex quadratic programming problem, SVMs can find the global optimal solution rather than local minima and avoid overfitting. SVMs have a strong theoretical foundation and good generalization performance. The algorithm is based on limited sample information and can provide real-time results. Originally, SVMs were developed for solving binary classification problems. Recently, SVMs have been used for feature recognition in ground-penetrating radar (GPR) images. SVMs are capable of identifying features in GPR images with scarce data in nonlinear and high-dimensional problems [16]. Through-wall radar is similar to GPR, so we address through-wall problems using an SVM. Several studies of this method have been conducted, and the results were satisfactory. Wang and Zhang [17, 18] were able to estimate the location and the electromagnetic characteristics of the target, but the method failed to produce a clear image of the target. Other studies have performed human activity classification based on micro-Doppler signatures [19, 20], but the methods used require that the target is moving and thus do not work with a static target. To obtain an image of a target, we f (...truncated)