-
根据压缩感知原理,稀疏信号可基于少量的观测进行重构。因此,存在冗余的信号可按此原理进行有效降维。参考文献[25]根据这一理论设计了随机投影算法并在特征提取和目标识别中进行了应用。为进一步处理图像等二维数据,参考文献[26-27]将一维的投影矩阵延伸到二维。以图像分析为例,输入图像
$X \in {{{R}}^{{n_1} \times {n_2}}}$ 经过两个随机投影矩阵${A} \in {{{R}}^{{m_1} \times {n_1}}}$ 和${B} \in {{{R}}^{{m_2} \times {n_2}}}$ ,按照$ {Y} = {AX}{{B}^{\text{T}}} $ 的方式变换得到特征矩阵${Y} \in {{{R}}^{{m_1} \times {m_2}}}$ ,其中$ {m_1} $ 远小于$ {n_1} $ ,$ {m_2} $ 远小于$ {n_2} $ ,实现高效降维。根据参考文献[26]相关论述,为了使得二维投影后的特征矩阵能够有效保持图像特性,要求通过低维度的投影矩阵
$ Y $ 能够对原始图像进行高精度重构。此时,需要对两个投影矩阵进行如下约束:$$ {\left\| {X} \right\|_0} < {\text{spark}}({A}){\text{spark}}({B})/4 $$ $$ ({\ell _0}{\text{ norm of each column of }}{X}) < {\text{spark}}({A})/2 $$ $$ ({\ell _0}{\text{ norm of each row of }}{X}) < {\text{spark}}({B})/2 $$ (1) 式中:
$ {\left\| {X} \right\|_0} $ 计算$ {X} $ 的$ {\ell _0} $ 范数,即为矩阵中非零元素的个数;函数$ {\text{spark}} $ 获取当前矩阵中相互独立的列数。对于矩阵${A} \in {{{R}}^{{m_1} \times {n_1}}}$ 和${B} \in {{{R}}^{{m_2} \times {n_2}}}$ ,满足$ {\text{spark}}({A}) = {m_1} + 1 $ ,$ {\text{spark}}({B}) = {m_2} + 1 $ 。基于上述准则构造的二维随机投影矩阵可有效获取SAR图像的鉴别力特征,并已成功应用于目标识别。然而,这种特征提取方法由于投影矩阵的不唯一性而具有一定的随机性,导致识别结果存在不稳定的问题。为此,文中采用若干个二维随机投影矩阵对原始图像进行处理。不同投影矩阵下的结果具有互补性,可有效弥补单一投影矩阵存在的不稳定。因此,联合不同投影矩阵下的结果有利于提供最终的识别性能。
-
传统典型相关分析(Canonical correlations analysis,CCA)主要用于比较两组随机变量,分析它们之间的关联性和差异。MCCA则是对传统CCA进行延伸扩展,主要用于分析多组不同随机变量之间的关联性和差异[23-24]。记一组随机变量为
$ {X_1},{X_2}, \cdots ,{X_n} $ ,它们的维度分别为$ {m_1},{m_2}, \cdots ,{m_n} $ ($ {m_1} $ 为最小值)。MCCA算法首先对各个随机变量进行去均值和中心化。然后,设计如公式(2)所示的准则函数:$$ {J_{{\text{MCCA}}}}({\alpha _1},{\alpha _2}, \cdots ,{\alpha _n}) = \frac{{\displaystyle\sum\limits_{i = 1}^n {\displaystyle\sum\limits_{j = 1}^n {\alpha _i^{\text{T}}{S_{ij}}{\alpha _j}} } }}{{\sqrt {\displaystyle\sum\limits_{i = 1}^n {\alpha _i^{\text{T}}{S_{ii}}{\alpha _i}} } }} $$ (2) 式中:
$ {S_{ij}} = E({X_i}X_j^{\text{T}}) $ 计算$ {X_i} $ 与$ {X_j} $ 两个随机变量的互协方差矩阵。为了对这一准则函数进行最大化,开展以下优化过程:$$ \mathop {\max }\limits_{{\alpha _1},{\alpha _2}, \cdots ,{\alpha _n}} \sum\limits_{i = 1}^n {\sum\limits_{j = 1}^n {\alpha _i^{\text{T}}{S_{ij}}{\alpha _j}} } $$ $$ {\text{s}}{\text{.t}}{\text{. }}\sum\limits_{i = 1}^n {\alpha _i^{\text{T}}{S_{ii}}{\alpha _i}} {\text{ = }}1 $$ (3) 对于公式(3)的优化过程,可利用Lagrange乘子法进行求解:
$$ \left( {\begin{array}{*{20}{c}} {{S_{11}}}& \ldots &{{S_{1n}}} \\ \vdots & \ddots & \vdots \\ {{S_{n1}}}& \cdots &{{S_{nn}}} \end{array}} \right)\left( \begin{gathered} {\alpha _1} \\ \vdots \\ {\alpha _n} \\ \end{gathered} \right) = \left( {\begin{array}{*{20}{c}} {{\lambda _1}{S_{11}}}& \ldots &0 \\ \vdots & \ddots & \vdots \\ 0& \cdots &{{\lambda _n}{S_{nn}}} \end{array}} \right)\left( \begin{gathered} {\alpha _1} \\ \vdots \\ {\alpha _n} \\ \end{gathered} \right) $$ (4) 根据对公式(4)的求解结果进一步获取变换矩阵
$ A = {[{\alpha _1},{\alpha _2}, \cdots ,{\alpha _n}]^{\text{T}}} $ ,其中:$$ \begin{gathered} {\alpha _1} = {\left[ {{\alpha _{11}},{\alpha _{12}}, \cdots ,{\alpha _{1{m_1}}}} \right]_{{m_1} \times {m_1}}} \\ {\alpha _2} = {\left[ {{\alpha _{21}},{\alpha _{22}}, \cdots ,{\alpha _{2{m_1}}}} \right]_{{m_2} \times {m_1}}} \\ {\text{ }} \vdots \\ {\alpha _n} = {\left[ {{\alpha _{n1}},{\alpha _{n2}}, \cdots ,{\alpha _{n{m_1}}}} \right]_{{m_n} \times {m_1}}} \\ \end{gathered} $$ (5) 对应地,从公式(5)中可以得到不同变量
$ {X_i} $ 对应的投影方向,采用公式(6)对不同随机变量加权融合,得到结果如下:$$ Z = \alpha _1^{\text{T}}{X_1} + \alpha _2^{\text{T}}{X_2} + \cdots + \alpha _n^{\text{T}}{X_n} $$ (6) 文中采用MCCA对同一幅SAR图像的多个不同特征进行融合。最终获取的特征矢量不仅能保持不同投影矩阵的独立性,也可以去除可能存在的冗余或干扰成分。因此,融合后的特征矢量具有更强的鉴别力和简洁性,有利于提高识别算法的整体性能。
-
自稀疏表示理论提出和应用以来,其衍生工具在信号、图像处理等领域得到十分广泛的运用。SRC就是一个典型代表,主要用于模式识别中监督分类问题[17-19]。对于多类别的训练样本,可根据它们建立全局字典
$A = [{A_1},{A_2}, \cdots ,{A_C}] \in {{{R}}^{d \times N}}$ ,其中$ {A_i} $ 对应来自第$ i $ 类中$ {N_i} $ 个训练样本。测试样本$ y $ 在全局字典上进行线性表示,求解线性表示系数:$$ \hat x = \mathop {\arg \min }\limits_x {\left\| x \right\|_0} $$ $$ {\text{s}}{\text{.t}}{\text{. }}\left\| {y{{ - }}Ax} \right\|_2^2 \leqslant \varepsilon $$ (7) 式中:
$ x $ 为需要求解的系数矢量;$ \varepsilon $ 为误差门限。根据现有文献,上述非凸优化问题可通过
$ {\ell _{\text{1}}} $ 范数替代$ {\ell _0} $ 范数进行转换,从而简化优化问题,获取近似解。此外,也可采用正交匹配追踪等贪婪算法进行寻优。根据系数求解结果,可以按照公式(8)分别阶段单个类别的重构误差大小:$$ r(i) = \left\| {y{{ - }}{A_i}{x_i}} \right\|_2^2(i = 1,2, \cdots ,C) $$ (8) 式中:
$ {x_i} $ 为第$ i $ 类上的系数矢量;$ r(i){\text{ }} $ 即为$ i $ 类别的最终误差。最后,可以根据误差判定测试样本与哪一类训练样本最为相似,从而获得类别决策结果。 -
根据前文思想,文中设计如图1所示的目标识别流程,实线部分代表训练流程,虚线部分代表测试流程,中间部分为相同流程,具体实施描述如下。首先,按照二维随机投影的构造原则获取若干对随机投影矩阵,用于对SAR图像的特征提取。对于训练样本,分别采用不同的投影矩阵进行特征提取,进一步采用MCCA对它们进行融合,获得单一的特征矢量,存入全局字典。据此可构建与训练样本规模一致的全局字典。对于测试样本,按照上述步骤经随机投影特征提取和MCCA特征融合获得对应的特征矢量。最终,采用SRC对测试样本的特征矢量进行分类,判决目标所属类别。
图 1 基于二维随机投影特征MCCA融合的自动目标识别流程
Figure 1. Procedure of ATR based on MCCA of 2D random projection features
二维随机投影矩阵在无需先验知识的情况下,保持了SAR图像的二维结构信息。同时,结合多个不同二维随机投影矩阵的结果,能够实现对目标特性互补的描述,进一步增强特征层的鉴别力。基于MCCA的特征融合有效继承了多层次二维随机投影特征的优势,同时去除了存在的冗余分量。SRC中的稀疏重构分类机制具有较强的噪声、遮挡稳健性,采用其进行最终决策有利于提高识别结果的稳健性。因此,文中方法通过结合特征提取和分类决策的优势提升整体识别性能。
-
在SAR目标识别领域,MSTAR数据集具有很强的代表性,是当前绝大多数相关方法开展验证的基础数据集。MSTAR计划中,研究人员在多种场景和操作条件下采集了图2所示的10类目标的SAR图像,分辨率达到0.3 m。据此,可分别构建训练和测试样本,验证目标识别算法的有效性。根据现有文献报道,在MSTAR数据集的样本基础上可设置诸如标准操作条件、目标型号差异、俯仰角差异等测试条件。此外,通过对原始MSTAR样本进行简单处理,可进一步构建噪声干扰、部分遮挡等测试条件。文中在上述条件中重点对标准操作条件、俯仰角差异以及噪声干扰三种场景进行针对性实验,检验提出方法的有效性和稳健性。
实验中还设置了一些对比方法,它们包括参考文献[25]基于随机投影的方法(Random projection),该方法采用一维随机投影算法进行SAR图像降维;参考文献[26]中二维随机投影的方法(记为2D random projection),该方法将一维投影扩展到二维,从而更好地保持图像结构信息;参考文献[8]采用单演信号特征的方法(记为Monogenic),结合不同成分特征进行决策;参考文献[20]中基于CNN的方法(记为CNN),该方法针对SAR目标识别设计了特定结构的CNN。
-
标准操作条件是SAR目标识别问题中一项基础且具有代表性意义的实验场景。根据MSTAR数据集包含的目标类别和不同条件下的SAR图像数据,设置表1所示的测试条件,且每个目标只有一种型号。测试集为各类目标15°俯仰角下的样本,其中BMP2和T72两类目标各包含3个型号。对比训练和测试集,两种样本虽然存在一定差异但整体相似度较高,可认为是标准操作条件。对于10类目标的识别结果,采用平均识别率进行定量评价,即正确识别样本数所占的比例。据此,表2对比了不同方法的识别性能。文中方法以99.08%的平均识别率优于四类对比方法。CNN方法性能排名第二,显示了深度学习网络优越性能。二维随机投影方法的性能优于传统的一维随机投影方法,体现了二维特征提取的必要性。相比单演信号方法,二维随机投影方法略有劣势,主要是特征鉴别力的差距。然而,单演信号特征分解的复杂度要远远高于二维随机投影。文中方法在多层次二维随机投影特征的基础上进行融合处理,经过MCCA过后的特征矢量显著提升了识别性能,反映了方法设计思路的科学性。
表 1 标准操作条件的样本设置
Table 1. Sample settings for SOC
Target label Training set (Depression: 17°) Test set (Depression: 15°) Configuration Samples Configuration Samples BMP2 9563 218 9563
9566
c21180
181
181BTR70 - 218 - 181 T72 132 217 132
812
s7181
180
176T62 - 284 - 258 BRDM2 - 283 - 259 BTR60 - 241 - 180 ZSU23/4 - 284 - 259 D7 - 284 - 259 ZIL131 - 284 - 259 2 S1 - 284 - 180 表 2 标准操作条件下的对比结果
Table 2. Comparison results under SOC
Method Proposed Random projection 2D random projection Monogenic CNN Average recognition rate 99.08% 97.18% 98.23% 98.64% 98.82% -
在上述标准操作条件中,一个重要的因素是测试样本与训练样本的俯仰角差异很小。实际上,测试样本很可能来自于测试样本差距较大俯仰角,此时两者的图像差异也会较为明显。根据MSTAR数据集中的SAR图像数据,设置如表3所示的训练和测试集。训练集包含了2S1、BRDM2以及ZSU23/4共3类目标在17°俯仰角下的SAR图像。测试样本来自差异较大的俯仰角,可进一步区分为两个子集,分别对应30°俯仰角和45°俯仰角。两个测试子集反映了不同程度的俯仰角差异,能够更为全面地反映方法在不同俯仰角差异程度条件下的识别性能。基于上述设置,获取不同方法的识别性能,统计如表4所示。从两个测试子集的角度来看,30°俯仰角下的整体性能要明显优于45°,反映了大俯仰角差异带来的识别难度急剧增加。根据上述结果,文中方法对于不同程度俯仰角差异的适应性和稳健性更强,能够在俯仰角差异的情形下保持良好性能。相比标准操作条件,CNN方法在此条件下的性能下降最为剧烈,表明在训练样本不足或与测试样本差异较大时,深度学习算法也存在很大的局限性。文中方法通过MCCA对多层次的二维随机投影特征进行融合,可获取稳健的识别性能,确保了在此场景下的性能。
表 3 俯仰角差异的样本设置
Table 3. Sample settings for depression angle variance
Target label Training set Test set Depression/(°) Samples Depression/(°) Samples 2 S1 17 284 30
45283
288BRDM2 17 283 30
45272
288ZSU23/4 17 284 30
45273
288表 4 俯仰角差异下的结果对比
Table 4. Comparison results under depression angle variances
Method Average recognition rate 30° 45° Proposed 96.87% 72.19% Random projection 94.72% 68.52% 2D random projection 95.14% 69.52% Monogenic 95.73% 70.42% CNN 95.32% 68.34% -
图像噪声水平直接影响图像质量,低信噪比(Signal-to-noise ratio,SNR)的图像会给识别问题带来很大难度。原始MSTAR数据集的SAR图像整体信噪比较高,据此建立的训练和测试集具有相接近的噪声惠普,因此难以评价方法在测试样本不同信噪比条件下的识别性能。为此,文中按照参考文献[12]的思路和方法对表1中的测试样本进行噪声条件,以原始图像为参照分别构建多个不同信噪比(含−10 dB、−5 dB、0 dB、5 dB和10 dB)的样本测试集。然后,就不同信噪比下的测试样本对各类方法进行测试,获得如图3所示的平均识别率曲线。伴随信噪比的降低,各类方法的平均识别率均出现了较为明显的下降,充分反映了噪声干扰的影响。对比几类方法,文中方法可在不同噪声水平保持最佳性能,具有最强的噪声稳健性。与俯仰角差异的情况类似,CNN方法由于样本不足,导致性能下降十分剧烈。与二维随机投影方法相比,文中通过多个随机投影矩阵的联合使用和有效的特征融合显著提升了对于噪声干扰的稳健性。
SAR ATR method based on canonical correlations analysis of features extracted by 2D random projection
-
摘要: 合成孔径雷达(Synthetic aperture radar,SAR)自动目标识别(Automatic target recognition,ATR)是现代战场情报侦察、精确打击的重要支撑技术。为提升SAR ATR整体性能,提出基于二维投影特征多重集典型相关分析(Multiset canonical correlations analysis,MCCA)的方法。首先,采用若干二维随机投影矩阵对SAR图像进行特征提取,获得多层次特征描述。考虑到这些结果之间的相关性和可能存在的冗余及干扰,进一步通过MCCA对它们进行融合处理,获取单一特征矢量。基于稀疏表示分类器(Sparse representation-based classification,SRC)对融合特征矢量进行处理,判决目标类别。实验基于MSTAR数据集开展,对方法性能进行检验确认,结果能够验证其有效性。Abstract: Synthetic aperture radar (SAR) automatic target recognition (ATR) is an important support technology for modern battlefield intelligence reconnaissance and precision strikes. In order to improve the overall performance of SAR ATR, a method based on multiset canonical correlations analysis (MCCA) of two-dimensional (2D) projection features is proposed. First, a series of 2D random projection matrices are used to extract features from SAR images to obtain multi-level feature descriptions. Considering the correlation between these results and the possible redundancy and interference, they are further fused through MCCA to obtain a single feature vector. The sparse representation-based classification (SRC) is used to process the fusion feature vector to determine the target class. The experiment is carried out based on the MSTAR dataset to fully test the proposed methods. The experimental results verify its effectiveness.
-
表 1 标准操作条件的样本设置
Table 1. Sample settings for SOC
Target label Training set (Depression: 17°) Test set (Depression: 15°) Configuration Samples Configuration Samples BMP2 9563 218 9563
9566
c21180
181
181BTR70 - 218 - 181 T72 132 217 132
812
s7181
180
176T62 - 284 - 258 BRDM2 - 283 - 259 BTR60 - 241 - 180 ZSU23/4 - 284 - 259 D7 - 284 - 259 ZIL131 - 284 - 259 2 S1 - 284 - 180 表 2 标准操作条件下的对比结果
Table 2. Comparison results under SOC
Method Proposed Random projection 2D random projection Monogenic CNN Average recognition rate 99.08% 97.18% 98.23% 98.64% 98.82% 表 3 俯仰角差异的样本设置
Table 3. Sample settings for depression angle variance
Target label Training set Test set Depression/(°) Samples Depression/(°) Samples 2 S1 17 284 30
45283
288BRDM2 17 283 30
45272
288ZSU23/4 17 284 30
45273
288表 4 俯仰角差异下的结果对比
Table 4. Comparison results under depression angle variances
Method Average recognition rate 30° 45° Proposed 96.87% 72.19% Random projection 94.72% 68.52% 2D random projection 95.14% 69.52% Monogenic 95.73% 70.42% CNN 95.32% 68.34% -
[1] EL-Darymli K, Gill E W, Mcguire P, et al. Automatic target recognition in synthetic aperture radar imagery: a state-of-the-art review [J]. IEEE Access, 2016, 4: 6014-6058. doi: 10.1109/ACCESS.2016.2611492 [2] Anagnostopoulos G C. SVM-based target recognition from synthetic aperture radar images using target region outline descriptors [J]. Nonlinear Analysis, 2009, 71(2): 2934-2939. [3] Papson S, Narayanan R M. Classification via the shadow region in SAR Imagery [J]. IEEE Transactions on Aerospace and Electronic System, 2012, 40(8): 969-980. [4] Mishra A K, Motaung T. Application of linear and nonlinear PCA to SAR ATR[C]// Radioelektronika, 2015: 1-6. [5] LI W H, Wang J G. SAR images target recognition based on bilateral two-dimensional principal component analysis and probabilistic neural network ensemble [J]. Journal of CAEIT, 2014, 9(4): 401-407. (in Chinese) doi: 10.3969/j.issn.1673-5692.2014.04.015 [6] Cui Z Y, Cao Z J, Yang J Y, et al. Target recognition in synthetic aperture radar via non-negative matrix factorization [J]. IET Radar, Sonar and Navigation, 2015, 9(9): 1376-1385. doi: 10.1049/iet-rsn.2014.0407 [7] Dong G G, Kuang G Y, Wang N, et al. SAR target recognition via joint sparse representation of monogenic signal [J]. IEEE Journal of Selected Topics Applied Earth Observation and Remote Sensing, 2015, 8(7): 3316-3328. doi: 10.1109/JSTARS.2015.2436694 [8] Wang Y Y. SAR target recognition based on monogenic features via multiset canonical correlation analysis [J]. Electronics Optics & Control, 2019, 26(10): 7-11,29. (in Chinese) doi: 10.3969/j.issn.1671-637X.2019.10.002 [9] Liu X W, Lei J J, Wu Y P. Synthetic aperture radara target recognition based on bidimensional empirical mode decomposition [J]. Laser and Optoelectronics Progress, 2020, 57(5): 051004. (in Chinese) [10] Zhou G Y, Liu B Q, Zhang D. Target recognition in SAR images based on variational mode decomposition [J]. Remote Sensing for Land and Resources, 2020, 32(2): 33-39. (in Chinese) [11] Zhang R, Hong J, Ming F. Full polarimetry SAR ATR algorithm based on polarimetry similarity [J]. Foreign Electronic Measurement Technology, 2010, 29(5): 24-27. (in Chinese) doi: 10.3969/j.issn.1002-8978.2010.05.005 [12] Ding B Y, Wen G J, Yu L S, et al. Matching of attributed scattering center and its application to synthetic aperture radar automatic target recognition [J]. Journal of Radar, 2017, 6(2): 157-166. (in Chinese) [13] Ding B Y, Wen G J, Zhong J R, et al. A robust similarity measure for attributed scattering center sets with application to SAR ATR [J]. Neurocomputing, 2017, 219: 130-143. doi: 10.1016/j.neucom.2016.09.007 [14] Hao Y, Ai Y P, Zhang Y F. Synthetic aperture radar target recognition based on KNN [J]. Fire Control & Command Control, 2018, 43(9): 113-115, 120. (in Chinese) [15] Liu C Q, Chen B, Pan Z H, et al. Research on Target Recognition Technique via Simulation SAR and SVM classifier [J]. Journal of CAEIT, 2016, 11(3): 257-262. (in Chinese) doi: 10.3969/j.issn.1673-5692.2016.03.008 [16] Liu H C, Li S T. Decision fusion of sparse representation and support vector machine for SAR image target recognition [J]. Neurocomputing, 2013, 113: 97-104. [17] Thiagaraianm J, Ramamurthy K, Knee P P, et al. Sparse representations for automatic target classification in SAR images [C]//4th Communications, Control and Signal Processing, 2010: 1–4. [18] Tang J S, Qin S H. SAR target recognition based on sparse coefficients optimal local reconstruction [J]. Journal of Detection & Control, 2013, 43(2): 69-75. (in Chinese) [19] Zhang H, Zuo X L, Huang Y. Feature selection based on the correlation of sparse coefficient vectors with application to SAR target recognition [J]. Laser and Optoelectronics Progress, 2020, 57(14): 141029. (in Chinese) [20] Chen S Z, Wang H P, Xu F, et al. Target classification using the deep convolutional networks for SAR images [J]. IEEE Transactions on Geoscience and Remote Sensing, 2016, 54(8): 4806-4817. doi: 10.1109/TGRS.2016.2551720 [21] Zhang P P, Luo H B, Ju M R, et al. An improved capsule and its application in target recognition of SAR images [J]. Infrared and Laser Engineering, 2020, 49(5): 20201010. (in Chinese) doi: 10.3788/irla.26_invited-zhangpanpan [22] Xu Y, Gu Y, Peng D L, et al. SAR ATR based on disentangled representation learning generative adversarial networks and support vector machine [J]. Optics and Precision Engineering, 2020, 28(3): 727-735. (in Chinese) doi: 10.3788/OPE.20202803.0727 [23] Peng J L, Li Q, El-latif A A, et al. Linear discriminant multi-set canonical correlations analysis (LDMCCA): an efficient approach for feature fusion of finger biometrics [J]. Multimedia Tools and Applications, 2015, 74(13): 4469-4486. doi: 10.1007/s11042-013-1817-x [24] Qiu A K, Zhu J G. Multi-set canonical correlations analysis based on ensemble learning [J]. Computer Engineering and Applications, 2017, 53(6): 162-169. (in Chinese) doi: 10.3778/j.issn.1002-8331.1510-0147 [25] Zhang H C, Nasrabadi N M, Zhang Y, et al. Multi-view automatic target recognition using joint sparse representation [J]. IEEE Transactions on Aerospace and Electronic Systtems, 2012, 48(3): 2481-2497. [26] Ding B Y, Wen G J, Ye F, et al. Feature extraction based on 2 D compressive sensing for SAR automatic target recognition [C]//EUCAP, 2017: 1219-1223. [27] Wu J B, Lu Z W, Guang Y R, et al. SAR target recognition using feature fusion by 2D compressive sensing with multiple random projection matrices [J]. Infrared and Laser Engineering, 2021, 50(6): 20200531. (in Chinese)