Convolutional neural network-based perturbation shooting and bouncing rays solution for recognition of targets with uncertain geometrical shapes

Abstract

We fabricated an effective target recognition network-based on the convolutional neural network and the perturbation Shooting and Bouncing Rays algorithm for electrically large targets having varying geometrical shapes. The algorithm started by constructing a relationship between the local random variables and target's geometry by using the non-uniform rational B-spline surface modeling method. Inverse synthetic aperture radar (ISAR) imaging was performed quickly for perturbed geometrical shapes and the algorithm can achieve higher computational efficiency than the Monte Carlo method. The ISAR imaging database was generated, and the database can describe the local geometrical uncertainty of the target. All the ISAR imaging results were used to train the CNN-based training network. When an ISAR image of a target with an uncertainty shape was inputted, this target could be recognized via the proposed CNN-based target recognition network. Our numerical results proved that the recognition rate could go up to 90% even for complicated targets.

Introduction

In recent years, inverse scattering has been widely applied in remote sensing [1], medical imaging [2] and fault detection [3]. There are two main difficulties in the application of inverse scattering: nonlinear and ill-posed problems [4]. In general, it is difficult to acquire unique and accurate solutions for the inverse scattering problems. There are two methods for solving the inverse scattering problems, namely, the quantitative method and qualitative method [5]. The quantitative method can achieve accurate results, but it needs a large amount of computational resources. The qualitative methods lessen the computational burden but provide only morphological and no electromagnetic information about the target [6]. A convolutional neural network (CNN) is a promising tool for solving the inverse problems arising from its generalization ability, and it increases the availability of large databases [7]. For example, the DeepNIS [8] methodology has been proposed to find the connection between the deep CNNs and iterative methods for electromagnetic (EM) inverse scattering. Also, a U–net–based deep neural network [9] has been proposed for the EM inverse scattering problems.

An important step in the CNN identification network is the construction of the database. A good method of identifying targets is by using inverse synthetic aperture radar (ISAR) imaging to construct the database. The ISAR imaging technique has been long used to fast classify and identify the targets [10]. Fast and accurate acquisition of the radar echoes is the key to the ISAR imaging technique. There are two dominating numerical methods to solve the EM problems, namely, the rigorous full-wave analysis method [11] and the high-frequency approximate method [12]. Although the rigorous full-wave method can provide an exact solution, the high-frequency approximate method is widely used because of its high efficiency and encouraging accuracy. More specifically, the shooting and bouncing rays (SBR) method is one of the most popular schemes, and it is based on geometrical optics and physical optics. The SBR method was firstly proposed for solving the cavity scattering problems [12]. Later, it was used to analyze the EM scattering from the arbitrary objects having electrically large features [13]. Although the SBR method is effective, tracing the ray tube is time-consuming because numerous ray tubes are required for electrically large targets. Therefore, improved SBR methods have been proposed to reduce the computational resources, such as muti-resolution grid algorithm [14], graphics processing unit-accelerated SBR method [15], and the open graphics library-accelerated SBR method [16]. In the recent years, some novel SBR-based numerical methods have been proposed to improve the accuracy of the traditional SBR method. In [17], an improved SBR, physical optics hybrid method was proposed to reduce the computation complexity. An efficient volumetric SBR method was proposed in [18] to improve the accuracy for analyzing the scattering from plasma sheath. For the traditional imaging method, the monostatic scattering fields are required for a range of angles and frequencies [19]. As a result, large computational resources are needed. Therefore, many fast imaging methods (FIMs) have been proposed to accelerate the calculations, such as compressive sensing multilevel fast multipole algorithm -based FIM [20] and the fast Fourier transform (FFT)-based FIM [21]. The FFT-based FIM is a good choice for acquiring the ISAR image because of it does not need to sweep the angles and frequency. In this way, the database of the ISAR image can be constructed quickly.

However, all the above imaging methods cannot rapidly provide the live images when the shapes of the target vary. Therefore, the study of uncertainties is very important. Because of the loss of information, there are some uncertainties (shapes, materials etc.) in the computational EMs. The Monte Carlo (MC) method [22] is the most popular tool, but it results in excessive computational burdens. Many methods have been proposed to enhance the convergence of the MC method, such as the quasi-MC method [23], Markov Chain MC method [24], and stratified sampling method [25]. However, it is inefficient to solve complex problems with multiple random elements. Therefore, a generalized polynomial chaos method [26] was proposed to alleviate the problems having multiple uncertainties. There are two traditional schemes, namely, stochastic Galerkin scheme [27] and stochastic collocation scheme [28]. These schemes can improve the accuracy. To describe the uncertainties, the non-uniform rational B-spline (NURBS) surface modeling approach was proposed to model the varying geometric targets [[29], [30]]. Then, to find an efficient method for detecting the relationship between the random variables and scattering properties, we proposed a stochastic method that handles the scattering of targets with varying shapes [[31], [32]]. The varying of the target shapes can be described by several variables in the computational equations of the combined field integral equation. Therefore, the scattering properties of the target can be derived by the perturbation approach using less computational resources than the traditional MC method [[31], [32]]. In this way, the uncertain EM scattering properties can be easily acquired.

In this paper, an efficient SBR-based imaging method is proposed to fast identify the electrically large targets with varying shapes. The algorithm starts by describing the target with several random variables using the NURBS surface modeling approach. Then, the random variables are easily implemented in the SBR-based fast-imaging equations. In this way, the ISAR database can be effectively constructed for electrically large targets with varying shapes. Finally, the convolution neural network (CNN) was applied for classification and identification because it has good generalization ability for small samplings [33]. The numerical results demonstrate the efficiency of the proposed method. In the first example, we analyzed the scattering from a missile with varying wing thickness to verify the accuracy of the proposed SBR-based uncertainty analytical method. Then, we compared the proposed SBR-based FIM with the traditional imaging method to demonstrate the efficiency of the proposed method, which was used to construct the database. Finally, the identification rate was tested for six kinds of aircrafts by using the CNN. We found that the identification rate went up to 90% even for complex targets.