Improvement of Attributed Scattering Center Extraction by Using SAR Super-Resolution Preprocessing

Guozhen Cheng, Jiacheng Chen, Fengming Hu, Feng Xu

Abstract: Synthetic aperture radar (SAR) is able to acquire high-resolution method using the active microwave imaging method.SAR images are widely used in target recognition, classification,and surface analysis, with extracted features.Attribute scattering center (ASC) is able to describe the image features for these tasks.However, sidelobe effects reduce the accuracy and reliability of the estimated ASC model parameters.This paper incorporates the SAR super-resolution into the ASC extraction to improve its performance.Both filter bank and subspace methods are demonstrated for preprocessing to supress the sidelobe.Based on the preprocessed data, a reinforcement based ASC method is used to get the parameters.The experimental results show that the super-resolution method can reduce noise and suppress sidelobe effect, which improve accuracy of the estimated ASC model parameters.

Keywords: synthetic aperture radar (SAR); spectrum estimation; attributed scattering center(ASC); reinforcement learning

1 Introduction

Synthetic aperture radar (SAR) is able to map earth surface with high resolution.Since SAR operates in the microwave portion of the electromagnetic spectrum, it is able to to overcome limitations posed by cloud cover, darkness, and adverse weather conditions, making it a versatile tool for various applications.

In some practical applications, such as radar-based material identification, classification [1], surface analysis [2], and object recognition [3,4], these all depend on accurate feature extraction.While traditional target feature extraction methods mainly focus on the image domain [5].The ideal point scattering model used only has the characterization ability of isolated scatterers, but lacks the characterization of frequency dependence and angle dependence [5].As a result, the model can only roughly extract the geometric shape features reflecting the target,but cannot provide shape dependent parameters,and thus cannot fully characterize the essential properties of the target [6].The electromagnetic characteristics of the target can be described using either mathematical or physical models.The established electromagnetic model shows the relationship between the scattering center and the target physical component, which enables an accurate description of physical properties [7,8].Feature extraction based on electromagnetic scattering model directly extracts its genus from the scattering response of the target information avoids information loss in the process of intermediate links [8], and fully characterizes the frequency and angle of the target.The degree and polarization-dependent characteristics are more conducive to target identification [9].

Attributed scattering center extraction(ASC) involves identifying and characterizing discrete scattering centers within a SAR image[10].Scattering centers are individual points or areas on a target that contribute significantly to the radar echo received by the SAR system [11].These centers possess unique characteristics that can help differentiate between different types of targets and their physical properties [12].ASC methods attempt to isolate these scattering centers and extract information about their attributes, which could include location, size, shape,and radar cross-section (reflectivity) [13].

ASC techniques play a crucial role in SAR image interpretation and understanding complex scenes [10,13].They can enhance target discrimination and enable more accurate target recognition and classification [14].However, the challenges posed by sidelobe effects, along with factors like noise and complex terrain, need to be carefully addressed to ensure the reliability of the extracted scattering center attributes.

2-D SAR focusing algorithms (such as range Doppler algorithm (RDA), range migration algorithm (RMA) [15,16], etc.) requires both range and azimuth FFT for original raw data respectively.Since the limited range of the two-dimensional frequency domain support in the range and azimuth direction [17], sidelobe appears in the target SAR image, which might be erroneously interpreted as scattering centers or targets, leading to the generation of false attribute information.In the context of ASC applications, this could result in the misestimation of target attributes, thereby impacting target classification and identification.This concern becomes particularly pertinent when the target closely resembles its surroundings or when the target’s resolution is low.Sidelobe effects could potentially mask genuine target features, making their accurate extraction and analysis challenging [18].

In order to address the impact of sidelobe effects in ASC applications, a spectral estimation approach is employed for super-resolution imaging to mitigate the interference caused by sidelobes [19].This technique involves enhancing image resolution by analyzing the spectral information of the signal.In this paper, two methods,Capon [20] and multiple signal classification(MUSIC) [21], are utilized to process the twodimensional SAR images [17].Subsequently, the processed images are subjected to ASC.By improving the resolution of the images through spectral analysis, ASC can then yield more accurate and reliable information about the scattering centers, aiding in better target understanding and characterization.

2 Methodology

According to the frequency modulated continuous wave (FMCW) SAR imaging model [22], the imaging problem of FMCW SAR can be transformed into a 2-D complex sinusoidal signal parameter estimation problem.The signal model of applying spectral estimation method in radar imaging processing is

wherex(m,n) is the sampling data after preprocessing andm=0,...,M-1,n= 0,...,N-1.Range frequency of Scatterpisωrp, azimuth frequency isωap, and complex backscattering coefficient issp.The numberDof signal components is determined by the estimation method of signal sources numbers.At first, the frequency parameter (position)θ=(ωr,ωa) of target point is estimated.Then the backscatter coefficients of target point can be estimated according to the expected parameterθi=(ωr,i,ωa,i)D i=1.In this paper, Filter bank method and Subspace orthogonal decomposition method are studied.

2.1 Filter Bank Method

The filter bank method is a general term for a series of methods, which used to analyze a signal’s frequency content across multiple frequency bands.It involves decomposing a signal into various subbands using a set of filters that have specific frequency ranges [23].The Capon method,also known as minimum variance distortionless response (MVDR) , is one of the filter bank methods for spectral estimation.It is commonly applied in the field of signal processing to enhance signal resolution and suppress noise[20,24].

In the following formulation, lowercase boldface italic characters refer to vectors while uppercase boldface italic characters refer to matrices.For either real- or complex-valued matrices, (.)*will be used to denote the Hermitian conjugate(or complex-conjugate transpose) operation.

For simplicity, the one-dimensional formulation is presented.Assuming theNobservationszT=[z1,...,zN] , then theMpoints filter with center frequencyωis

This algorithm constructs a bank of adaptive bandpass finite impulse-response filters with a length ofM.Then a bank of filtershω1,...,hωNis expected.Such filter can be applied on all observations and produces a response only at its central frequencyω

Ris the covariance matrix of the observations,we define the vector of data sampleszl=[zl zl+1...zl+M-1]T, the number of the samplesL=N-M+1,Yis

andRis computed by

Finally, we get the new estimation [20]

The Capon filter constructs a set of filters with the property that the energy passing through the filter is as small as possible.So the response only contains a single frequency component.The corresponding manifestation is in the spectrum, where a spike appears and the sidelobe is suppressed.

2.2 Subspace Orthogonal Decomposition Method

This method make eigen-decomposition on the autocorrelation matrix of signal and use the eigenvectors as a set of orthogonal vectors to construct a linear space [25].Multiple signal classification (MUSIC) method is a typical algorithm of subspace orthogonal decomposition method for spectral estimation.MUSIC makes eigen-decomposition on covariance matrix of the data to obtain the signal subspace corresponding to the signal component and the noise subspace orthogonal to the signal components [21,26].Then the two orthogonal subspaces are used to estimate the signal parameters.For the high resolution of MUSIC method under a certain condition, it is widely used in super-resolution information processing.

The signal observation model of MUSIC method can be expressed as

where data vectorx(k)=[x1(k)...xL(k)]Tis the received data fromLspatial array elements in thektimes,n(k)=[n1(k)...nL(k)]Tis noise vector,s(k)=[s1(k)...sL(k)]Tis composed ofDsignal vectors,L×Ddimensional matrix.A=[a(ω1)...a(ωD)]Tanda(ω) is steering vector.

We assume that the signal and noise are independent [21], the data covariance matrix can be decomposed into two independent orthogonal subspaces:

The dimension of the signal subspace isDand the dimension noise subspace isL×D.The basic column vectors of noise subspace can be constitute the matrixUN, and the spectral peak searching of MUSIC method is as follows [21]

We assume that SAR image is a 2-D spectrum and 2-D IFFT is firstly applied on the image.Then the data is reshaped to get theYmatrix and adopt the process described in Sections 2.1 and 2.2.Fig.1 shows the process flow of a single chip image [5].

Fig.1 The process flow of MUSIC and Capon

2.3 ASC

2.3.1 ASC Model

Two-dimensional attributed scattering center model describes the dependence of the backward scattering field of the target scattering center on frequency and azimuth under monostatic condition in the high-frequency region.The expression of a single attributed scattering center is[6,11,12,27]

The backscattered field is modeled by a concise set of seven parametersθ=(A,α,x,y,L,φ,γ),the physical meaning of which is clear.αis taken as one of {-1, -0.5, 0, 0.5, 1} here, according to the values ofLandα, the scattering centers can be simply classified into seven types as listed in Tab.1 [6,13,27].The total backscattered field of a complex target can be expressed as the superposition ofPattributed scattering centers while adding the noise [6,27].

whereEiis the scattering field of each single scattering center, andNis the noise matrix.Retrieval of the number of scattering centersPand the parametersθiof each scattering center from the total scattering fieldEof is an illposed and multiplicity problem.Considering the sparsity of the scattering centers of scattering field,the scattering center extraction is represented as a sparse representation problem to obtain a feasible solution.The above equation (12) can be equivalent to solving followingL0norm optimization problem defined as follows [6,11,12].

wheresis the vectorized total scattering,Dis an overredundant dictionary generated according to the ASCM parameters collectionΘ=θ1,θ2,...,θi,...,θQ,σis a sparse vector with non-zero valuesAiin a few positions,nis vectorized noise matrix.

Tab.1 Scattering center types [6]

2.3.2 A Reinforcement Learning Method for ASC

Almost all the traditional ASC parameter estimation methods lack an efficient parameter update strategy, since the large parameter space brings great algorithm complexity.The proposed reinforcement learning approach enable a efficient parameter estimation by modeling the repetitive iterative process of parameter optimization as the interaction process between the agent and the environment [28].This algorithm can significantly improved the efficiency while the accuracy of the algorithm is guaranteed and is able to extract ASC parameters from measured data effectively.It modeled the form of iterative optimizations as an RL environment [29], where its interaction framework is illustrated in Fig.2.The training dataset is generated randomly with the parameters of SNR, number and position of scatterers.The agent can choose the actions to take at each time step, which will change the state of the environment in an unknown way, and receive feedback based on the results of the actions, and the cumulative reward function is defined as

whereγtis the reward intstep,γ ∈(0,1] is discount factor.Thus, the parameter of next interaction Θi+1=Θi+ΔΘiis obtained [30].More details of this method is shown in [28].

Fig.2 Interaction flow in the single scattering center parameter retrieval

3 Results

3.1 Super-Resolution Results

Three dataset are used to evaluate the algorithms.The first demonstration, a simulation data is used to test the algorithms.The simulation data parameters is set as shown in Tab.2.The corresponding results are shown in Fig.3.Fig.3(d) shows that Capon reduces the noise to a certain extent compared with the original simulation data Fig.3(a), but the scatterer centers cannot be identified clearly.Fig.3(g) shows the result that processed by MUSIC.It greatly reduces the noise of the image, and greatly weakens the sidelobe, so that the dense scatterers can be well distinguished.

Tab.2 Simulation data parameters

The second demonstration, we test the algorithms on a measured airborne SAR data.Fig.3(b)shows the corner reflector SAR image, showing significant sidelobe and noise.Similar to previous results, the performance of noise reduction by capon is weaker than that by MUSIC.Fig.4 shows the measured data PSF in range and azimuth.Both Capon and MUSIC can suppress the sidelobe, and MUSIC even has better performance compared with Capon.

Fig.3 Preprocessed results using spectral estimation methods: (a) simulation data; (b) measured data in Tianjin; (c) data from MSTAR; (d)(e)(f) results used Capon method; (g)(h)(i) results used MUSIC method

Fig.4 PSF of the super-resolution result use Tianjin data: (a) Azimuth PSF; (b) Range PSF

The third demonstration is conducte using the MSTAR dataset.The data were collected by the Sandia National Laboratory SAR sensor platform.The collection was jointly sponsored by the Defense Advanced Research Projects Agency and the Air Force Research Laboratory as part of the MSTAR program [31].Hundreds of thousands of SAR images containing ground targets were collected, including different target types, aspect angles, depression angles, serial number, and articulation, and only a small subset of which are publicly available on the website [32].The dataset provides a variety of different types of radar images, including images from different angles, different polarizations, and different target types, as well as real data containing noise and clutter, which shown in Fig.3(c).Fig.3 (f)and (i) are the results of Capon and MUSIC processing results.MUSIC does better not only noise reduction but also sidelobe suppression.

The performance of MUSIC and Capon varies with the scene.Based on the concept of signal subspace and noise subspace, MUSIC can obtain signal subspace by calculating the eigenvalue decomposition of signal and noise covariance matrix.In contrast, Capon relies on the inverse of the covariance matrix, and its calculation process can produce numerical instability in the case of low signal noise.MUSIC and Capon may show different strengths in different situations.Capon method can better deal with the balance between signal and noise, and is suitable for the case of relatively low signal noise.On the other hand, the MUSIC method may be more accurate in the case of high SNR.Which method should be chosen depends on the needs of the particular application and the signal environment.

3.2 ASC Results

Based on the proposed reinforcement learning approach, the ASC parameters of the three dataset are obtained correspondingly.Note that the residuals between the original and the reconstructed image vary with the radar imaging process, which cannot be used for the evaluation.So we only focus on the difference between the estimated and the true ASC parameters.In the simulated and measured dataset, we have the actual ASC parameters since the types of the targets are known.

The experimental results of simulation data show that the preprocessing algorithm is helpful for the ASC inversion algorithm to decouple the scattering centers with tight spatial distribution,as shown in Fig.5 (a)(d)(g).From the results of inversion parameters, it can be found by comparing the true values in the simulation that super-resolution preprocessing can improve the accuracy of scattering center position parameters,but it will increase the inversion errors of other information such as intensity.A feasible idea is to invert the position parameters only with the preprocessed image, and then fix the position parameters and invert other parameters on the original image.

The experimental of measured data results show that for ASC inversion of a single target,whether using MUSIC method or Capon method for pre-processing, it is better than direct inversion without processing.Fig.5(b) shows that due to the influence of sidelobe, the ASC inversion method in image domain will disassemble a single angular inverse target into multiple scattering centers by mistake.After MUSIC and Capon preprocessing as shown in Fig.5(e)(h),only one scattering center is obtained.The type of scattering center deduced by inversion parameters is angular inverse (L=0,α=1), which is consistent with the actual situation as shown in Tab.3.Moreover, Tab.3 shows that with Capon or MUSIC, the number of scatters is estimated more accuracy that less noise is estimated to signal by mistake.L,αare estimated almost with no errors.

For the measured data MSTAR, the inversion directly on the original image will also invert part of the background noise as the scattering center of the target as shown in Fig.5(c), which is eliminated by the two pretreatment methods.MUSIC preprocessing can assist ASC inversion algorithm to distinguish multiple scattering centers that are misidentified as one distributed scattering center.In contrast, Fig.5(f)(i) show that the Capon method makes it easier to weaken some weak scattering centers near the strong scattering centers, so that they are ignored by the inversion algorithm.

Fig.5 Rebuilt image based on parameter retrieval result of proposed method: (a)(b)(c) using the origin data rebuilt image based on parameter retrieval result of proposed ASC method; (d)(e)(f) and (g)(h)(i) results obtained using Capon and MUSIC

Tab.3 Estimated ASC parameters

In summary, the superresolution preprocessing algorithm has the following conclusions for ASC inversion in the image domain: 1) It can eliminate most of the side lobes and noise effects on inversion results; 2) Both the MUSIC method and the Capon method are applicable to scattering centers with sparse spatial distribution; 3)For images with dense scattering centers, the MUSIC method is more suitable; 4) It can improve the accuracy of scattering center location parameters, but it will also lead to an increase in errors related to the inversion of intensity and other information; 5) In order to better apply to the ASC parameter inversion task, only the pre-processed image can be used to invert the position parameters, and then other parameters can be inverted on the original image.

4 Conclusion

In this study, we implemente the Capon and MUSIC algorithms to achieve super-resolution reconstruction of SAR images and incorporates this process into the ASC parameters estimation.These super-resolution algorithms effectively suppresses noise and sidelobe present in the original images.The experimental results demonstrate a significant improvement in the accuracy and reliability of retrieving the scattering center information.Typically, Capon could reduces noise and suppresses sidelobe without the need to set additional hyperparameters, but need much compute resources, and poor performance in the case of low SNR condition.Compared with Capon,MUSIC has better performance, but such performance improvement depends on selecting a suitable noise subspace size.So optimal noise subspace size should be investigated in the future work.