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摘要: 合成孔径雷达自动目标识别(SAR-ATR)领域缺乏有效的黑盒攻击算法，为此，该文结合动量迭代快速梯度符号(MI-FGSM)思想提出了一种基于迁移的黑盒攻击算法。首先结合SAR图像特性进行随机斑点噪声变换，缓解模型对斑点噪声的过拟合，提高算法的泛化性能；然后设计了能够快速寻找最优梯度下降方向的ABN寻优器，通过模型梯度快速收敛提升算法攻击有效性；最后引入拟双曲动量算子获得稳定的模型梯度下降方向，使梯度在快速收敛过程中避免陷入局部最优，进一步增强对抗样本的黑盒攻击成功率。通过仿真实验表明，与现有的对抗攻击算法相比，该文算法在MSTAR和FUSAR-Ship数据集上对主流的SAR-ATR深度神经网络的集成模型黑盒攻击成功率分别提高了3%～55%和6%～57.5%，而且生成的对抗样本具有高度的隐蔽性。Abstract: The field of Synthetic Aperture Radar Automatic Target Recognition (SAR-ATR) lacks effective black-box attack algorithms. Therefore, this research proposes a migration-based black-box attack algorithm by combining the idea of the Momentum Iterative Fast Gradient Sign Method (MI-FGSM). First, random speckle noise transformation is performed according to the characteristics of SAR images to alleviate model overfitting to the speckle noise and improve the generalization performance of the algorithm. Second, an AdaBelief-Nesterov optimizer is designed to rapidly find the optimal gradient descent direction, and the attack effectiveness of the algorithm is improved through a rapid convergence of the model gradient. Finally, a quasihyperbolic momentum operator is introduced to obtain a stable model gradient descent direction so that the gradient can avoid falling into a local optimum during the rapid convergence and to further enhance the success rate of black-box attacks on adversarial examples. Simulation experiments show that compared with existing adversarial attack algorithms, the proposed algorithm improves the ensemble model black-box attack success rate of mainstream SAR-ATR deep neural networks by 3%～55% and 6%～57.5% on the MSTAR and FUSAR-Ship datasets, respectively; the generated adversarial examples are highly concealable.
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图 6 黑盒模型下攻击成功率变化折线图
Figure 6. Line chart of attack success rate change under black-box model
图 7 TBAA干净样本、对抗扰动以及对抗样本展示
Figure 7. TBAA clean examples, adversarial perturbations and adversarial examples display
1 基于迁移的SAR-ATR黑盒攻击算法
1. SAR-ATR Transfer-based Black-box Attack Algorithm (TBAA)
输入：干净样本x，K个深度神经网络模型${f_1},{f_2},\cdots,{f_K}$，对应
的网络模型逻辑值${l_1},{l_2},\cdots,{l_K}$以及相应的网络模型集成权重
${w_1},{w_2},\cdots,{w_K}$，扰动量大小$\varepsilon $，步长$\alpha $，迭代次数T，系数$v,\beta $,
${\beta _1}$和${\beta _2}$输出：对抗样本${x^{{\text{adv}}}}$ 步骤1 $\alpha \leftarrow \varepsilon /T,{g_0} \leftarrow 0,{m_0} \leftarrow 0,{n_0} \leftarrow 0$ 步骤2 ${g_0} \leftarrow 0,{m_0} \leftarrow 0,{s_0} \leftarrow 0,x_0^{{\text{adv}}} \leftarrow x$ 步骤3 For $t = 0$ to $T - 1$ do 步骤4 Update ${m_t}$ by ${m_t} = {\beta _1} \cdot {m_{t - 1}} + (1 - {\beta _1}){g_t}$ 步骤5 Update ${\hat m_t} = \dfrac{{{m_t}}}{{1 - \beta _1^t}}$ 步骤6 Update ${s_t} = {\beta _2} \cdot {s_{t - 1}} + (1 - {\beta _2}){({\hat g_t} - {m_t})^2}$ 步骤7 Update ${\hat s_t} = \dfrac{{{s_t} + \zeta }}{{1 - \beta _2^t}}$ 步骤8 $ \tilde x_t^{{\text{adv}}} = x_t^{{\text{adv}}} + \dfrac{\alpha }{{\sqrt {{{\hat s}_t} + \zeta } }}{\hat m_t} $ 步骤9 $l(\tilde x_t^{{\text{adv}}}) = \sum\limits_{k = 1}^K {{w_k}{l_k}\left( {{\text{ST}}(\tilde x_t^{{\text{adv}}};p)} \right)} $ 步骤10 Update $g_t^*$ by $ g_t^* = {\nabla _{x_t^{{\text{adv}}}}}J\left( {{\text{ST}}(\tilde x_t^{{\text{adv}}};p),y} \right) $ 步骤11 Update ${g_{t + 1}}$ by ${g_{t + 1}} = \beta {g_t} + (1 - \beta ) \cdot \dfrac{{g_t^*}}{{{{\left\| {g_t^*} \right\|}_1}}}$ 步骤12 Update ${\tilde g_{t + 1}}$ by ${\tilde g_{t + 1}} = (1 - v){g_{t + 1}} + v \cdot \dfrac{{g_t^*}}{{{{\left\| {g_t^*} \right\|}_1}}}$ 步骤13 $x_{t + 1}^{{\text{adv}}} = {\mathrm{Clip}}_x^\varepsilon \left\{ {x_t^{{\text{adv}}} + \alpha \cdot {\mathrm{sign}}({{\tilde g}_{t + 1}})} \right\}$ 步骤14 End for 步骤15 Return $x_t^{{\text{adv}}} = x_{t + 1}^{{\text{adv}}}$ 
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表 1 MSTAR数据中SOC下的SAR图像类别与样本数量
Table 1. SAR image categories and number of samples under SOC in MSTAR dataset
目标类别 训练集 测试集 俯仰角(°) 数量 俯仰角(°) 数量 2S1 17 299 15 274 BRDM2 17 298 15 274 BTR60 17 233 15 195 D7 17 299 15 274 T62 17 299 15 273 ZIL131 17 299 15 274 BMP2 17 233 15 195 ZSU23/4 17 299 15 274 T72 17 232 15 196 BTR70 17 233 15 196
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表 2 FUSAR-Ship数据集中SAR图像类别与样本数量
Table 2. SAR image categories and number of samples in FUSAR-Ship dataset
目标类别 训练集数量 测试集数量 BulkCarrier 97 25 CargoShip 126 32 Fishing 75 19 Tanker 36 10
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表 3 模型识别精度
Table 3. Model recognition accuracy
模型 MSTAR ACC (%) FUSAR-Ship ACC (%) AlexNet 95.1 69.47 VGG16 95.6 70.23 ResNet18 96.6 68.10 ResNet50 97.7 — InceptionV3 99.1 — A-ConvNet 99.8 — MobileNet 97.8 — SqueezeNet 95.4 72.25 PVTv2 98.8 — MobileViTv2 99.4 72.70
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表 4 MSTAR数据集单模型攻击成功率(%)
Table 4. Single model attack success rate on the MSTAR dataset (%)
代理模型 攻击算法 受害者模型 AlexNet VGGNet16 ResNet18 ResNet50 InceptionV3 A-ConvNet MobileNet SqueezeNet PVTv2 MobileViTv2 AlexNet MI-FGSM 100* 10.9 12.0 9.0 5.0 28.0 35.0 18.9 14.0 19.6 NAM 100* 12.0 13.0 10.0 6.9 36.0 37.0 22.9 20.7 22.0 VMI-FGSM 100* 19.5 19.5 17.0 6.0 29.5 39.5 27.0 40.5 21.5 DI-FGSM 100* 21.0 26.5 16.0 7.5 29.5 43.5 32.5 32.0 20.5 Attack-Unet-GAN 98.69* 7.0 8.0 7.5 4.0 20.5 32.5 14.5 12.5 9.5 Fast C&W 100* 4.5 7.0 6.0 3.0 17.5 19.5 12.5 8.0 3.5 TBAA 100* 23.5 29.0 20.4 14.5 64.0 53.4 33.9 56.0 32.8 VGGNet16 MI-FGSM 61.0 100* 58.0 56.0 40.0 55.0 41.0 43.0 26.0 30.0 NAM 60.0 100* 61.0 59.0 42.0 61.0 45.0 47.0 31.0 35.0 VMI-FGSM 62.5 100* 59.5 58.5 42.5 57.5 41.0 46.5 38.5 38.5 DI-FGSM 63.5 100* 60.5 67.5 46.5 59.5 42.5 48.0 37.5 38.5 Attack-Unet-GAN 53.0 100* 40.5 32.5 24.5 32.5 38.5 39.0 23.0 24.5 Fast C&W 44.5 100* 31.0 37.5 24.0 31.5 22.0 24.5 13.5 14.5 TBAA 69.5 100* 72.0 78.5 56.9 74.0 56.5 63.5 48.0 48.5 ResNet18 MI-FGSM 13.0 9.9 100* 20.9 13.9 39.0 26.0 15.0 14.0 5.0 NAM 15.0 9.0 100* 20.9 16.0 38.0 31.0 17.0 21.0 5.3 VMI-FGSM 17.0 16.5 100* 25.0 15.8 45.5 31.5 25.0 32.5 10.5 DI-FGSM 18.0 14.0 100* 21.0 19.0 41.0 29.5 30.0 23.5 8.6 Attack-Unet-GAN 12.5 6.5 100* 11.5 5.0 19.5 18.5 11.5 11.0 3.0 Fast C&W 10.0 4.0 100* 6.0 3.0 9.0 11.5 12.0 13.5 4.0 TBAA 29.0 19.0 100* 25.0 35.5 64.0 42.5 30.0 54.0 24.0 ResNet50 MI-FGSM 8.0 12.0 10.5 100* 21.0 16.0 22.9 10.0 12.0 9.0 NAM 10.0 14.0 14.0 100* 22.0 27.0 24.0 13.0 17.0 14.9 VMI-FGSM 19.5 19.0 14.5 100* 22.0 33.0 33.5 21.0 28.5 13.5 DI-FGSM 19.5 19.0 22.5 100* 23.5 26.5 23.0 22.5 28.0 11.5 Attack-Unet-GAN 6.5 10.5 6.5 100* 7.0 15.0 18.0 8.0 8.0 7.0 Fast C&W 5.0 4.5 7.5 100* 13.0 7.5 10.5 7.5 10.5 6.0 TBAA 24.5 19.9 27.5 100* 27.4 48.5 44.9 25.5 43.9 22.0 InceptionV3 MI-FGSM 29.0 31.4 65.5 38.0 100* 65.0 31.0 39.0 12.0 28.0 NAM 36.0 35.0 67.9 42.0 100* 66.9 33.9 41.9 18.0 29.5 VMI-FGSM 33.0 31.5 52.5 39.0 100* 68.5 34.0 43.0 30.0 29.5 DI-FGSM 34.0 34.5 56.0 41.0 100* 66.0 33.5 41.5 23.5 28.5 Attack-Unet-GAN 20.6 24.5 53.0 31.0 100* 32.5 25.0 26.5 9.0 24.5 Fast C&W 11.0 16.5 30.0 28.0 100* 20.0 12.0 15.0 10.5 16.5 TBAA 41.0 50.0 73.5 52.0 100* 76.5 49.5 47.0 45.9 43.9 A-ConvNet MI-FGSM 19.9 15.5 29.5 20.9 11.5 100* 29.0 15.0 21.9 9.0 NAM 23.5 17.5 35.5 24.5 18.9 100* 32.5 18.0 24.0 13.0 VMI-FGSM 25.5 19.0 37.0 25.5 19.5 100* 36.5 31.0 31.0 12.5 DI-FGSM 28.0 17.5 37.0 23.0 21.5 100* 36.5 29.5 26.5 10.5 Attack-Unet-GAN 10.8 5.6 9.0 13.0 7.0 98.0* 11.6 11.0 14.7 8.0 Fast C&W 11.5 4.0 8.5 5.0 3.0 97.5* 10.5 12.5 13.5 4.0 TBAA 29.5 21.9 40.5 30.5 24.5 100* 38.0 32.9 36.0 24.0 MobileNet MI-FGSM 16.0 15.1 10.0 15.0 15.6 18.0 100* 18.9 8.0 9.0 NAM 18.0 14.9 12.0 18.9 18.9 25.0 100* 26.9 9.5 10.5 VMI-FGSM 21.0 18.0 12.0 18.0 21.5 23.0 100* 23.5 22.0 14.0 DI-FGSM 19.0 17.5 10.5 17.5 18.0 19.5 100* 20.5 22.0 14.5 Attack-Unet-GAN 9.0 3.5 7.5 7.8 2.5 12.5 100* 11.0 7.3 5.0 Fast C&W 10.0 4.0 6.0 5.0 3.0 7.0 100* 10.0 6.5 4.0 TBAA 24.0 20.5 18.9 26.0 25.4 32.9 100* 30.0 24.0 25.0 SqueezeNet MI-FGSM 19.5 9.5 20.5 18.0 6.0 40.5 31.4 100* 18.0 18.0 NAM 18.5 10.3 20.9 19.5 6.5 40.5 32.9 100* 24.0 21.0 VMI-FGSM 26.5 15.5 28.5 25.5 11.0 42.5 32.0 100* 28.5 19.5 DI-FGSM 21.0 11.5 30.5 22.5 12.0 41.0 31.5 100* 23.0 21.5 Attack-Unet-GAN 13.0 8.0 16.5 17.0 4.5 17.5 17.0 100* 12.5 14.5 Fast C&W 10.0 4.5 7.0 5.5 3.0 18.0 10.0 100* 13.5 14.0 TBAA 28.0 18.5 32.5 31.0 12.5 53.5 38.5 100* 41.9 39.0 PVTv2 MI-FGSM 10.0 7.3 9.0 12.0 15.5 6.0 18.0 7.8 100* 11.3 NAM 13.0 3.5 10.7 13.5 21.5 10.4 19.9 9.0 100* 18.5 VMI-FGSM 12.0 12.0 9.5 20.0 22.5 16.0 23.0 11.0 100* 19.5 DI-FGSM 11.0 13.5 11.0 15.0 23.5 12.0 23.5 12.6 100* 13.0 Attack-Unet-GAN 8.5 5.0 7.5 7.9 12.5 3.5 11.6 4.5 100* 9.0 Fast C&W 10.0 4.0 6.5 4.5 13.0 5.5 9.0 3.7 100* 4.0 TBAA 26.0 23.0 22.0 27.0 35.0 28.9 37.0 25.0 100* 32.0 MobileViTv2 MI-FGSM 14.0 16.0 19.0 18.3 7.9 43.8 30.0 18.0 52.0 100* NAM 21.4 24.0 26.2 20.7 11.6 47.8 33.9 25.4 58.0 100* VMI-FGSM 21.0 25.0 29.0 21.5 11.5 45.0 35.0 27.0 56.0 99.5* DI-FGSM 22.5 23.1 29.0 24.0 10.5 46.3 38.0 27.5 58.5 98.0* Attack-Unet-GAN 11.0 6.5 14.0 11.5 5.5 29.0 15.5 15.0 46.0 100* Fast C&W 11.0 4.0 8.5 5.5 3.0 17.5 10.5 11.5 45.0 99.5* TBAA 40.0 31.9 33.9 35.9 20.3 66.0 48.0 45.9 65.9 100* 注：标红字体为最优值，标蓝字体为次优值。*表示白盒攻击成功率，其余数值表示黑盒攻击成功率
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表 5 FUSAR-Ship数据集单模型攻击成功率(%)
Table 5. Single model attack success rate on the FUSAR-Ship dataset (%)
代理模型 攻击算法 受害者模型 AlexNet VGGNet16 ResNet18 SqueezeNet MobileViTv2 AlexNet MI-FGSM 100* 38.00 40.00 33.90 68.00 NAM 100* 48.00 62.00 45.90 76.00 VMI-FGSM 100* 47.10 63.60 42.60 70.00 DI-FGSM 98.41* 47.40 63.56 44.93 74.94 Attack-Unet-GAN 100* 23.80 33.20 15.60 30.00 Fast C&W 99.96* 18.70 29.10 12.40 24.00 TBAA 100* 60.00 84.00 56.00 80.00 VGGNet16 MI-FGSM 28.00 100* 24.00 40.00 46.00 NAM 33.90 100* 30.00 38.00 50.00 VMI-FGSM 33.90 98.62* 28.10 42.80 52.40 DI-FGSM 37.60 98.76* 36.60 42.40 52.60 Attack-Unet-GAN 13.50 100* 20.40 24.00 26.00 Fast C&W 9.30 99.96 19.60 22.90 24.00 TBAA 43.90 100* 48.00 62.00 56.00 ResNet18 MI-FGSM 6.00 7.90 100* 15.90 40.00 NAM 7.90 9.90 100* 21.90 50.00 VMI-FGSM 9.30 10.60 100* 28.60 53.80 DI-FGSM 13.50 12.80 99.96* 29.91 54.60 Attack-Unet-GAN 4.50 5.60 100* 10.40 17.80 Fast C&W 5.30 6.20 99.98* 6.70 12.90 TBAA 38.00 18.00 100* 50.00 60.00 SqueezeNet MI-FGSM 16.00 9.90 28.00 100* 45.90 NAM 21.90 14.00 43.90 100* 56.00 VMI-FGSM 25.10 19.30 44.20 99.86* 53.30 DI-FGSM 25.07 16.32 45.39 99.59* 59.40 Attack-Unet-GAN 14.50 7.90 22.00 100* 28.00 Fast C&W 10.10 6.30 20.10 98.69* 26.90 TBAA 39.90 31.90 65.90 100* 64.00 MobileViTv2 MI-FGSM 4.00 7.90 42.00 21.90 100* NAM 9.00 16.00 48.00 26.00 100* VMI-FGSM 12.80 23.50 45.90 24.10 100* DI-FGSM 13.20 18.60 47.00 26.40 99.52* Attack-Unet-GAN 2.90 5.30 25.60 18.00 100* Fast C&W 2.60 4.20 21.60 14.60 100* TBAA 24.00 16.00 67.90 43.90 100* 注：标红字体为最优值，标蓝字体为次优值。*表示白盒攻击成功率，其余数值表示黑盒攻击成功率
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表 6 集成模型攻击成功率(%)
Table 6. Ensemble model attack success rate (%)
数据集 攻击算法 AlexNet VGGNet16 ResNet18 ResNet50 InceptionV3 A-ConvNet MobileNet SqueezeNet PVTv2 MobileViTv2 MSTAR MI-FGSM 62.9 39.0 52.0 65.0 42.0 67.9 50.0 51.5 68.0 46.0 NAM 63.1 41.5 68.2 70.5 45.0 75.7 53.2 54.0 75.6 51.4 VMI-FGSM 66.4 43.5 72.5 65.8 46.5 74.6 52.0 53.0 76.3 56.0 DI-FGSM 69.0 44.3 74.0 70.0 50.3 76.0 55.0 55.8 70.0 51.0 Attack-Unet-GAN 53.6 30.5 47.0 35.0 30.0 35.0 41.0 43.0 52.3 31.0 Fast C&W 46.0 26.8 35.0 38.0 28.0 33.0 28.5 30.0 51.0 24.0 TBAA 72.0 62.0 86.0 88.0 70.0 88.0 70.0 66.0 92.0 78.0 FUSAR-
ShipMI-FGSM 31.9 40.9 48.0 — — — — 45.9 — 71.9 NAM 34.5 50.5 68.5 — — — — 48.5 — 78.0 VMI-FGSM 35.8 53.2 67.0 — — — — 51.3 — 76.5 DI-FGSM 36.0 56.0 68.0 — — — — 50.0 — 78.0 Attack-Unet-GAN 16.0 25.0 38.0 — — — — 28.5 — 38.4 Fast C&W 12.5 22.5 34.2 — — — — 26.0 — 32.0 TBAA 70.0 62.0 86.0 — — — — 64.0 — 88.0 注：标红数字为最优值，标蓝数字为次优值。
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表 7 消融实验方法设置
Table 7. Ablation experiment method setup
攻击算法 QHM ABN ST MI-FGSM — — — AN-QHMI-FGSM √ — — ABN-QHMI-FGSM √ √ — TBAA √ √ √
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表 8 消融实验攻击成功率(%)
Table 8. Ablation experiment attack success rate (%)
数据集 攻击算法 AlexNet VGGNet16 ResNet18 ResNet50 InceptionV3 A-ConvNet MobileNet SqueezeNet PVTv2 MobileViTv2 MSTAR MI-FGSM 62.9 39.0 52.0 65.0 42.0 67.9 50.0 51.5 68.0 46 AN-QHMI-FGSM 65.7 48.0 75.0 78.0 56.0 82.0 56.0 57.2 82.0 58.0 ABN-QHMI-FGSM 69.3 51.6 82.0 81.0 63.0 85.2 68.3 60.8 88.3 69.5 TBAA 72.0 62.0 86.0 88.0 70.0 88.0 70.0 66.0 92.0 78.0 FUSAR-
ShipMI-FGSM 31.9 40.9 38.0 — — — — 45.9 — 71.9 AN-QHMI-FGSM 36.9 52.0 76.0 — — — — 50.0 — 81.6 ABN-QHMI-FGSM 43.9 59.9 81.5 — — — — 52.0 — 85.0 TBAA 70.0 62.0 86.0 — — — — 64.0 — 88.0 注：标红数字为最优值，标蓝数字为次优值。
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表 9 MSTAR数据集在集成模型攻击下原始SAR图像和SAR对抗样本的平均结构相似度
Table 9. ASS of original SAR images and SAR adversarial examples under ensemble model attack on MSTAR dataset
攻击算法 AlexNet VGGNet16 ResNet18 ResNet50 InceptionV3 A-ConvNet MobileNet SqueezeNet PVTv2 MobileViTv2 Mean MI-FGSM 0.951 0.959 0.968 0.976 0.970 0.962 0.969 0.960 0.963 0.960 0.9638 NAM 0.962 0.965 0.971 0.978 0.973 0.967 0.973 0.966 0.968 0.962 0.9685 VMI-FGSM 0.965 0.961 0.972 0.976 0.975 0.969 0.977 0.967 0.969 0.965 0.9696 DI-FGSM 0.960 0.970 0.974 0.974 0.976 0.971 0.979 0.974 0.970 0.963 0.9711 Attack-Unet-
GAN0.968 0.975 0.975 0.978 0.978 0.974 0.982 0.975 0.972 0.968 0.9745 Fast C&W 0.969 0.974 0.976 0.979 0.979 0.974 0.980 0.975 0.971 0.967 0.9744 TBAA 0.969 0.975 0.979 0.981 0.978 0.975 0.981 0.973 0.972 0.967 0.9750 注：标红数字为最优值，标蓝数字为次优值。
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表 10 对抗样本生成效率(s)
Table 10. Adversarial examples generation efficiency (s)
攻击方法 VGGNet16 ResNet18 ResNet50 InceptionV3 A-ConvNet MobileNet Squeezenet Ensemble MI-FGSM 0.2970 0.2404 0.3621 0.5217 0.1797 0.3258 0.2550 1.8953 NAM 0.3014 0.2410 0.3623 0.5303 0.1822 0.3248 0.2257 1.8973 VMI-FGSM 0.2980 0.2498 0.3625 0.5289 0.1826 0.3289 0.2274 1.9766 DI-FGSM 0.2984 0.2485 0.3623 0.5280 0.1823 0.3283 0.2294 1.9795 Attack-Unet-GAN 0.0052 0.0052 0.0052 0.0052 0.0052 0.0052 0.0052 0.0052 Fast C&W 0.0053 0.0053 0.0053 0.0053 0.0053 0.0053 0.0053 0.0053 TBAA 0.3588 0.3046 0.4159 0.5676 0.2456 0.3876 0.2824 2.1357 注：标红数字为最大值，标蓝数字为最小值。
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