WANG Xinshuo, LU Jingyue, MENG Zhichao, et al. Forward-looking multi-channel synthetic aperture radar imaging and array attitude error compensation[J]. Journal of Radars, 2023, 12(6): 1155–1165. doi: 10.12000/JR23073
Citation: Li Yang, Lin Yun, Zhang Jing-jing, Guo Xiao-yang, Chen Shi-qiang, Hong Wen. Estimation and Removing of Anisotropic Scattering for Multiaspect Polarimetric SAR Image[J]. Journal of Radars, 2015, 4(3): 254-264. doi: 10.12000/JR15020

Estimation and Removing of Anisotropic Scattering for Multiaspect Polarimetric SAR Image

DOI: 10.12000/JR15020 CSTR: 32380.14.JR15020
  • Received Date: 2015-01-30
  • Rev Recd Date: 2015-04-16
  • Publish Date: 2015-06-28
  • Multiaspect Synthetic Aperture Radar (SAR) can generate high resolution images and target scattering signatures in different azimuth angles from the coherent integration of all subaperture images. However, mixed anisotropic scatters limit the application of traditional imaging theory. Anisotropic scattering may introduce errors in polarimetric parameters by decreasing the reliability of terrain classification and detection of variability. Thus a method is proposed for estimating and removing anisotropic scattering in multiaspect polarimetric SAR images. The proposed algorithm is based on the maximum likelihood and likelihood-ratio tests for the two-class case, while considering the speckle effect, the mechanism of removing the anisotropic scattering, and the monotonicity of the Constant False Alarm Rate (CFAR) detection function. We compare the polarimetric entropy before and after removing the anisotropic subapertures, and then validate the algorithm's potential in retrieving the target signature using a P-band quad-pol airborne SAR with circular trajectory.

     

  • High resolution radar imaging has been widely used in target scattering diagnostics and recognition. As we all know, high resolution in range dimension is derived from the bandwidth of the transmitting signal and in the cross range dimension from synthetic aperture of multiple spatial positions. Under the fixed bandwidth and the synthetic aperture, traditional Matched Filter (MF) based methods for radar imaging suffer from low resolution and high sidelobes limited by the synthetic aperture[1].

    In order to improve the resolution and suppress the sidelobes, many high resolution methods have been applied to radar imaging. For example, the recently introduced theory of Compressed Sensing (CS) provides an idea to improve the resolution and reduce the amounts of measurement data under the constraint of sparsely distributed target prior, which has been widely explored for applications of radar imaging[24]. However, conventional CS methods are confronted with a range of problems in practical scenarios, such as complexity in calculation, high Signal-to-Noise Ratio (SNR) requirement, model mismatch caused by off grid problem[5], phase mismatch[6], frequency error[7] and position error[8]. To avoid the off grid problem of CS, modern spectral estimation methods like MUltiple SIgnal Classification (MUSIC), matrix pencil and Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) have been used in radar imaging for resolution improvement[9]. However, most those methods suffer from performance degradation when there is little prior knowledge of the exact numbers of the scatters or under low SNR condition. Recently, the atomic norm minimization algorithm[10] based on continuous compressed sensing is introduced to enhance the SNR of the received echo and using Vandermonde decomposition to eliminate the grid mismatch. Nevertheless, this method can only be tailored to a specific model and brings huge computational cost.

    Consideration the aforementioned fact while combining the sparsity low rank matrix recovery technology and deconvolution algorithm, we introduce a high resolution radar imaging method based on the MF result. Firstly we establish the convolution model of target’s backscatter coefficients and the Point Spread Function (PSF), and then we want to use the deconvolution method like Wiener filter to improve the radar imaging resolution. However, the performance improvements of those methods depend on high SNR, and their super resolution performance is visibly affected by the low pass character of the PSF[11]. Although the MF result has enhanced the SNR, we can further improve the echo SNR by the sparsity and low rank matrix recovery. Low rank matrix recovery has been applied in many signal processing applications to estimate a low rank matrix from its noisy observation[12, 13]. Combinng the sparsity of the echo matrix, we modify the low rank matrix recovery and introduce it to radar echo denoising, which can improve the performance of the two-Dimensional (2D) deconvolution. Finally, some experimental results are conducted to verify the effectiveness of the proposed method.

    Notation: (·)T, (·)H and (·)* denote the transpose, the conjugate transpose and the conjugate operation, respectively. ,﹡, and ☉ indicate the inner product, the convolution and the Hadamard product. F, 1, are the Frobenius norm, sum of the absolute values and the nuclear norm.

    Considering a typical arrangement for radar imaging in which an object with scattering reflectivity σxy rotated by a scan angle θm (as shown in Fig. 1), we defined the positions of the transmitting and receiving antenna shown in a Cartesian coordinate as (W/2, –R, H) and (–W/2, –R,H), where W, R, H represent the antenna spacing, distance from antenna to XZ plane and XY plane, respectively.

    Figure  1.  Radar imaging geometry

    Transmitting a stepped-frequency signal with frequency fn and under Born approximation, the received scattered echo with Gauss noise Wmn is given by:

    Ymn=Sσxyej2πfnR(x,y;θm)/cdxdy+Wmn
    (1)

    In this equation: fn=f0+nΔf,n=0,1···,N1, f0 and Δf represent the start frequency and frequency step, θm=mΔθ,m=0,1,···,M, Δθ represents the rotating angle step, respectively. The range R(x,y;θm) from the transmitting antenna to echo scattering center and to the receiving antenna can be calculated as Eq. (2):

    R(x,y;θm)=(xcosθmysinθm+W2)2+(xsinθm+ycosθm+R)2+H2+(xcosθmysinθmW2)2+(xsinθm+ycosθm+R)2+H2
    (2)

    In far-field and small rotation angle case, R(x,y;θm) can be approximated by first order Taylor-series expansion as:

    R(x,y;θm)2(R0+(x+mΔθy)R/R0)
    (3)

    where R0=R2+(W/2)2+H2.

    Then the received echo can be written as follow under some approximated conditions:

    ˜Ymn=S˜σxyej4πRΔθλR0mxej4πRΔfR0cnydxdy+Wmn
    (4)

    where ˜σxy=σxyej4πRy/λR0, ˜Ymn=Ymnej4πfnR0/c, λc/f0.

    After discrete imaging region with P×Q grids, the received echo in Eq. (4) can be described as the following 2D linear signal model:

    ˜Y=Ax˜ΣATy+W
    (5)

    where ˜Y=[  ˜Ymn]M×N is the echo matrix, ˜Σ=[˜σpq]P×Q is the observation matrix: Ax=[ej4πmxpRΔθ/λR0]M×P, Ay=[ej4πnyqRΔf/R0c]N×Q.

    Considering the targets present sparse point scattering characteristic under high frequency scattering in most practical application scenarios, we present our method to improve the resolution of radar imaging under sparse target constraint using 2D deconvolution algorithm with low rank sparsity echo matrix denoising.

    As we all know, the MF algorithm which is based on the maximum signal to noise ratio is the most stable and commonly used radar imaging method. However, due to limitation of the synthetic aperture and bandwidth, the standard MF method suffers from relatively low resolution and high sidelobes, especially under the requirements of high resolution. The received echo after MF from Eq. (5) can be obtained by:

    YMF=AHx  ˜YAy
    (6)

    From the result of Eq. (6), the echo of the surface target after MF can be described as the sum of all the wave scattered at the points on the surface grid, i.e.,

    YMF(x,y)=xy˜σ(x,y)Psf(xx,yy)
    (7)

    where we define the PSF as:

    Psf(xx,yy)=ax(x),ax(x)ay(y),ay(y)
    (8)

    here, ax(x) and ay(y) represent the column of matrix Ax and Ay at the grid (x, y).

    We can find that Eq. (6) can be seen as the 2D convolution of the PSF and target backscatter coefficients:

    YMF(x,y)=˜σ(x,y)Psf(x,y)+WMF(x,y)
    (9)

    Inspired by this, we can recovery the backscatter coefficients using deconvolution algorithm to improve the imaging quality. Firstly, we should analyze the characteristic of the PSF and its influence on the deconvolution result.

    The PSF can be evaluated as:

    Psf(x,y)ej2π[(M1)RΔθλR0x+(N1)RΔfR0cy]sinc(2MRΔθλR0x)sinc(2NRΔfR0cy)

    (10)

    We can calculate the 2D mainlobe width which represents the radar imaging resolution as follows:

    ρx=λR02MRΔθ,ρy=R0c2NRΔf
    (11)

    Eq. (9) indicates that the MF result can be seen as the convolution result of backscatter coefficients and Psf(x,y). The PSF is characterized by synthetic aperture and bandwidth, which has strong low pass characteristic with low resolution and high sidelobes as shown in Eq. (10) and Eq. (11). For an isolated target scatter, imaging result after the MF output will be proportional to the PSF, therefore the resolution of MF result is limited and accompanied by low resolution and high sidelobes. Inspired by above, we can restore the high resolution backscatter coefficients information by deconvolution to remove the effect of low pass characteristic of PSF.

    As we have get 2D convolution form as Eq. (9), here we consider to use the direct deconvolution algorithm to recovery target backscatter coefficients. Firstly, we transform Eq. (9) into the spatial frequency domain using 2D Fourier transform as:

    Yω=ΣωHωω+Wω
    (12)

    where, Yω=F{YMF},Σω=F{˜Σ},Hω=F{Psf},Wω=F{WMF}.

    Theoretically, the target scattering information could be restored by deconvolution as:

    Σω=Yω/Hω
    (13)

    However, 1/Hω will be very large in practice at the outside of the mainlobe of PSF since the low pass characteristic of the PSF, which results in tremendous amplification of noise and obtains valueless results. So the deconvolution processing becomes an ill-posed inverse problem.

    In order to alleviate the ill-posed problem, we use Winner filtering algorithm and sparse low rank matrix recovery to improve the quality of imaging result.

    The result after Winner filter algorithm can be written as[14]:

    ˜Σω=YωHωHω2+ΨWW(ω)/ΨΣΣ(ω)
    (14)

    where ΨWW(ω) and ΨΣΣ(ω) is the power spectral density of W and Σ. Eq. (14) will approach Eq. (13) when the SNR is relatively high. What’s more, Eq. (14) will attenuate the high frequencies noise to alleviate the ill-posed problem under low SNR. In experimental data processing, the ΨWW(ω)/ΨΣΣ(ω) is generally set according to the experience value. We can get the scattering reflectivity ˜Σ by 2D Inverse Fourier transform according to Eq. (14).

    We can prove that the echo matrix after MF is sparse and low rank in Appendix A and by using this characteristic, the echo SNR can be improved. Consider the problem of estimating a sparse low rank matrix X from its noisy observation Y:

    Y=X+W
    (15)

    Define the sparse low rank matrix recovery problem as:

    minX,DγX+(1γ)D1subjecttoY=X+W,D=X
    (16)

    where γ is the regularization parameter used to balance the relative contribution between nuclear norm and the 1-norm, which can control the denoising performance. In general, the denoising threshold of γ can be set as the 5%~10% of the maximum singular value of Y.

    By applying Augmented Lagrangian Method (ALM), we can get the optimization problem:

    F(X,D,Y1,Y2,μ)=γX+Y1,YX+μ2YX2F+(1γ)D1+Y2,DX+μ2DX2F

    (17)

    And the update rules for solving this problem are as follows:

    X(k+1)=S(Y+D(k)2+Y(k)1+Y(k)22μ(k),γ2μ(k))
    (18)
    D(k+1)=soft(1μ(k)Y(k)2X(k+1),1γμ(k))
    (19)
    Y(k+1)1=Y(k)1+μ(k)(YX(k+1))Y(k+1)2=Y(k)2+μ(k)(D(k+1)X(k+1))μ(k+1)=βμ(k),β>1}
    (20)

    where, S(,) is the singular value thresholding function defined as:

    S(X,γ)=Usoft(Σ,γ)VT
    (21)

    where, X=UΣVT is the Singular Value Decomposition (SVD) of X, soft() is the soft thresholding function defined as:

    soft(x,γ)=sign(x)max{|x|γ,0}
    (22)

    See Appendix B for the detailed derivation of Eq. (18) and Eq. (19).

    The flowchart of the proposed method is shown in Fig. 2 by combining the sparse low rank matrix recovery with the 2D deconvolution.

    Figure  2.  The flowchart of the proposed method

    The parameters in the simulation are given in Tab. 1. In this experiment, we set four-point targets, the imaging results are shown in Fig. 3.

    Table  1.  Simulation parameters
    ParameterValueParameterValue
    M256R1 m
    N500H0.7 m
    Δf10 MHzW0.04 m
    Δθ0.009°SNR–15 dB
     | Show Table
    DownLoad: CSV
    Figure  3.  Imaging results

    As shown in Fig. 3(a), due to the limitation of synthetic aperture and bandwidth, the MF method suffers from relatively low resolution and high sidelobes which make it difficult to distinguish between four-point targets even there is no noise. Fig. 3(b)Fig. 3(d) show the imaging results reconstructed by MF and proposed method including the intermediate denoising results when SNR = –15 dB. It can be clearly seen that the effect of denoising compared Fig. 3(c) with Fig. 3(a) and Fig. 3(b), the echo SNR is further improved by the sparsity and low rank matrix recovery during the proposed intermediate denoising procedure. The final imaging result is shown in Fig. 3(d), from which we can see that the proposed method has a better reconstruction precision with higher resolution imaging of four distinguishable point targets.

    The experimental scene is shown in Fig. 4(a), which is the same with the model in Fig. 1. The radar system consists of a pair of horn antennas, a turntable whose rotation angle can be precisely controlled by the computer, and an Agilent VNA N5224A which is used for transmitting and receiving the stepped-frequency signal with bandwidth of 10 GHz from 28 GHz to 38 GHz and number of frequencies N equals to 256 (Frequency interval Δf is 40 MHz). Two kind of targets including three 5-mm-diameter mental spheres and a pair of scissors placed on a rotatory platform are used here as shown in Fig. 4(b).

    Figure  4.  Experimental scene VNA

    As we know, image entropy can be considered as a metric for measuring the smoothness of the probability density function of image intensities[15]. The imaging entropy is defined as:

    E(I)=Pp=1Qq=1|I2(p,q)s(I)|ln|I2(p,q)s(I)|
    (23)

    where s(I)=Pp=1Qq=1|I(p,q)|2.

    In this experiment, we set R=1m, H=0.7m,W=0.04m and the total rotating angle is 5 with an angle interval Δθ=0.01 (M=500).

    Fig. 5 shows the results of the MF and our proposed method for the mental spheres. The one-dimensional x and y domain cross-section of the target with red-dashed circle shown in Fig. 5 are presented in Fig. 6, in which the red-dashed line and blue line represent the result of MF and proposed method. Clearly, the reconstruction result of proposed method has a narrower main-lobe and lower side-lobe than MF and the sharpening ratio almost reach 5.8 and 3.0 in x and y domain, respectively.

    Figure  5.  Imaging results of mental spheres
    Figure  6.  One-dimensional cut through the target with red dashed circle in Fig. 5

    The parameters for this experiment are set as follows, R=0.876m, W=0.04m. The total rotating angle is 360 with M equals to 720. Taking into account the scintillation characteristics of the target under large rotating angle, we divide the rotating angle into 72 segments and each of the part is with rotating angle from 0 to 5. The proposed method is used to process the data for each segment and the image fusion method is used to merge the results of all segments.

    Fig. 7 shows the imaging results of the scissors reconstructed by MF and proposed method. It can be seen from the results that the proposed method has a high reconstruction precision with a shaper shape of scissors.

    Figure  7.  Imaging results of scissors

    The entropies of the imaging results by MF and our proposed method are given in Tab. 2 to quantitatively assess the performance. The proposed method has a low entropy which means the proposed method can improve the resolution and verifies its superiority.

    Table  2.  Entropies of imaging results
    TargetMFOur proposed method
    Mental spheres8.72824.8429
    Scissors8.94337.0454
     | Show Table
    DownLoad: CSV

    We introduce a robust deconvolution method with enhancing SNR technology to realize high resolution radar imaging. Compared to other high resolution methods, our proposed method is simple and robust. Although the signal model and experiments are performed for turntable radar situation with SF waveform, the method can be directly generalized to other practical radar systems based on other types of signals.

    Appendix A Proof of the sparsity and low rank characteristic

    To prove the echo matrix after MF is sparse and low rank, the following lemma is needed.

    Lemma 1[16]: For matrix A and B, the ranks of the product of A and B satisfy the inequality below:

    rank(AB)min{rank(A),rank(B)}
    (A-1)

    From Eq. (5) and Eq. (6), we can see that the echo matrix after MF can be written as:

    YMF =AHxAx˜ΣATyAy
    (A-2)

    We have supposed that the target has sparse distribution, so the target backscatter coefficients matrix ˜Σ is sparse and low rank. Thus, matrix YMF is also low rank according to lemma 1. The sparsity of matrix YMF can be proved by Eq. (9) obviously.

    Appendix B Derivation of Eq. (18) and Eq. (19)

    For Eq. (18), the optimization problem can be described as Eq. (B-1), and it has a closed-form solution just as Eq. (18) according to Ref. [13].

    X(k+1)=argminXF(X,D(k),Y(k)1,Y(k)2,μ(k))=argminX12X12(Y+D(k)+Y(k)1+Y(k)2μ(k))2F+γ2μ(k)X
    (B-1)

    For Eq. (19), it is the same with Eq. (18), which can written as

    D(k+1)=argminDF(X(k+1),D,Y(k)1,Y(k)2,μ(k))=argminD12D(Y(k)2μ(k)X(k+1))2F+1γμ(k)D1
    (B-2)

    It also has a closed-form solution as Eq. (19) according to Ref. [17].

  • [1]
    洪文. 圆迹SAR成像技术研究进展[J]. 雷达学报, 2012, 1(2): 124-135. Hong Wen. Progress in circular SAR imaging technique[J]. Journal of Radars, 2012, 1(2): 124-135.
    [2]
    Lee J S, Grunes M R, Pottier E, et al.. Unsupervised terrain classification preserving polarimetrics catteringcharacteristics[J]. IEEE Transactions on Geoscience and Remote Sensing, 2004, 42(4): 722-731.
    [3]
    Pottier E. Unsupervised classification scheme and topography derivation of PolSAR data based on the H/A/a polarimetric decomposition theorem[C]. Proceedings 4th International Workshop Radar Polarimetry, Nantes, France, 1998: 1-4.
    [4]
    Falconer D G and Moussally G J. Tomographic imaging of radar data gathered on a circular flight path about a threedimensional target zone[J]. SPIE, 2487: 2-12.
    [5]
    Soumekh M. Reconnaissance with slant plane circular SAR imaging[J]. IEEE Transactions on Image Processing, 1996, 5(8): 1252-1265.
    [6]
    Chan T K, Kuga Y, and Ishimaru A. Experimental studies on circular SAR imaging in clutter using angular correlation function technique[J]. IEEE Transactions on Geoscience and Remote Sensing, 1999, 37(5): 2192-2197.
    [7]
    Hubert M. Airborne SAR imaging
    [8]
    along a circular trajectory[C]. Sixth European Conference on Synthetic Aperture Radar, Dresden, Germany, 2006: 1-4. Oriot H and Cantalloube H. Circular SAR imagery for urban remote sensing[C]. Seventh European Conference on Synthetic Aperture Radar, Friedrichshafen, Germany, 2008: 1-4.
    [9]
    Ponce O, Prats-Iraola P, Pinheiro M, et al.. Fully polarimetric high-resolution 3-D imaging with circular SAR at L-band[J]. IEEE Transactions on Geoscience and Remote Sensing, 2014, 52(6): 3074-3090.
    [10]
    Lin Y, Hong W, Tan W, et al.. Extension of range migration algorithm to squint circular SAR imaging[J]. IEEE Geoscience and Remote Sensing Letters, 2011, 8(4): 651-655.
    [11]
    张祥坤. 高分辨率圆迹合成孔径雷达成像机理及方法研究[D].[博士论文], 中国科学院空间科学与应用研究中心, 2007. Zhang Xiang-kun. Study on imaging mechanism and algorithm of high-resolution circular SAR[D]. [Ph.D. dissertation], Center for Space Science and Applied Research Chinese Academy of Sciences, 2007.
    [12]
    刘燕, 吴元, 孙光才, 等. 圆轨迹SAR快速成像处理[J]. 电子与 信息学报, 2013, 35(4): 852-858. Liu Yan, Wu Yuan, Sun Guang-cai, et al.. Fast imaging processing of circular SAR[J]. Journal of Electronics Information Technology, 2013, 35(4): 852-858.
    [13]
    Runkle P, Nguyen L, McClellan J, et al.. Multi-aspect target detection for SAR imagery using hidden Markov models[J]. IEEE Transactions on Geoscience and Remote Sensing, 2001, 39(1): 46-55.
    [14]
    Ferro-Famil L, Reigber A, Pottier E, et al.. Scene characterization using subaperture polarimetric SAR data[J]. IEEE Transactions on Geoscience and Remote Sensing, 2003, 41(10): 2264-2276.
    [15]
    吴婉澜, 王海江, 皮亦鸣. 基于子孔径分析的极化散射机理研 究[J]. 雷达科学与技术, 2008, 6(4): 273-277. Wu Wan-lan, Wang Hai-jiang, and Pi Yi-ming. Study on polarimetric scattering bechavior based on subaperture analysis[J]. Radar Science and Technology, 2008, 6(4): 273-277.
    [16]
    Lee J S, Grunes M R, and Kwork R. Classification of multilook polarimetric SAR imagery based on complex Wishart distribution[J]. International Journal of Remote Sensing, 1994, 15(11): 2299-2311.
    [17]
    Lopez-Martinez C, Pottier E, and Cloude S. Statistical assessment of eigenvector-based target decomposition theorems in radar polarimetry[J]. IEEE Transactions on Geoscience and Remote Sensing, 2005, 43(9): 2058-2074.
    [18]
    王海江, 皮亦鸣, 杨小波. 极化SAR图像中基于子孔径分析的 两种非平稳目标检测[J]. 成都信息工程学院学报, 2012, 27(3): 243-246. Wang Hai-jiang, Pi Yi-ming, and Yang Xiao-bo. Two kinds of nonstationary targets detection in Pol-SAR images based on subaperture analysis[J]. Journal of Chengdu University of Information Technology, 2012, 27(3): 243-246.
    [19]
    Ulaby F T, Moore R K, and Fung A
    [20]
    K. Microwave Remote Sensing Active and Passive-Volume II: Radar Remote Sensing and Surface Scattering and Emission Theory[M]. USA: Addison-Wesley Publishing Company Advanced Book Program/World Science Division, 1982: 87-106.
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    • Table  1.  Simulation parameters
      ParameterValueParameterValue
      M256R1 m
      N500H0.7 m
      Δf10 MHzW0.04 m
      Δθ0.009°SNR–15 dB
       | Show Table
      DownLoad: CSV
    • Table  2.  Entropies of imaging results
      TargetMFOur proposed method
      Mental spheres8.72824.8429
      Scissors8.94337.0454
       | Show Table
      DownLoad: CSV