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A Hyperparameter-free Total Variation Regularization Method for Real Aperture Radar Angular Super-resolution
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摘要: 受平台物理空间限制，实孔径雷达天线波束宽、角分辨率低下。基于稀疏重建的角超分辨方法，在正则化框架下引入目标稀疏先验约束并通过迭代优化求解对目标散射分布进行反演，是提升实孔径雷达角分辨率的重要途径。然而，现有稀疏重建方法仅考虑了强点目标的稀疏分布特性，未考虑扩展目标的轮廓信息，存在目标边缘恢复失真的问题；同时，现有稀疏重建方法对代价函数中引入的超参数敏感，实际应用中依赖人工精细调整，难以根据不同场景进行自适应选取。针对上述两个问题，该文提出一种无超参数全变差(TV)正则化角超分辨方法，首先建立一种均方根LASSO代价函数，用于表征扫描回波序列与目标散射分布的拟合残差，以及目标边缘梯度的稀疏约束，从而将目标轮廓重建问题重转化为TV正则化约束下的非平滑凸优化问题；然后基于协方差拟合准则，导出了无超参数TV正则化约束的解析表达；最后提出一种广义迭代重加权最小二乘(GIRLS)求解策略，实现了均方根LASSO非平滑凸优化问题的迭代优化求解。仿真和实测结果表明，该文提出的方法能够在改善分辨率的同时保持目标的轮廓信息，且无需人工调整超参数。Abstract: A real aperture radar has physical space limitations that result in a wide antenna beam, leading to low angular resolution. The angular super-resolution method based on sparse reconstruction introduces sparse prior constraints of the target under a regularization framework and reconstructs the target reflectivity function through iterative optimization, thereby significantly enhancing the angular resolution of the radar. However, existing sparse reconstruction methods primarily consider the sparse distribution characteristics of strong point targets, neglecting the contour information of extended targets, which results in distortion in the recovery of target edges. Additionally, these methods are sensitive to one or more hyperparameters introduced into the cost function. Thus, meticulous manual adjustments are essential in practical applications, and they pose challenges in terms of the adaptive selection of hyperparameters in dynamic scenarios. To address these issues, this paper proposes a hyperparameter-free Total Variation (TV) regularization angular super-resolution method. First, a square-root Least Absolute Shrinkage and Selection Operator (LASSO) cost function was established to characterize the fitting residuals between the scan echo sequence and target reflectivity function and to characterize the sparse constraints on the target edge gradients. Using this function, the target contour reconstruction problem was transformed into a non-smooth convex optimization problem under TV regularization constraints. The analytical expression of the hyperparameter-free TV regularization term was derived based on the covariance fitting criterion. Finally, a Generalized Iteratively Reweighted Least Squares (GIRLS) strategy was proposed, and an iterative optimization method for solving the non-smooth convex optimization problem of square-root LASSO was derived. The simulation and experimental results demonstrate that the proposed method improves angular resolution of the radar while preserving the contour information of the target without requiring manual adjustment of the hyperparameters.
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图 2 各方法在不同信噪比下的MSE对比结果
Figure 2. MSE comparison of various methods under different SNRs
图 3 各方法在不同信噪比下的平均尺度测量误差对比结果
Figure 3. Average scale measurement error comparison of various methods under different SNRs
图 5 机载雷达正前视成像几何示意图
Figure 5. Illustration of forward-looking imaging geometry for airborne radar
1 基于GIRLS的迭代优化求解方法流程
1. Flowchart of the GIRLS-based iterative optimization solving method
1. 根据天线方向图向量h构造字典矩阵$ {\boldsymbol{B}} = {\boldsymbol{H}}{\nabla ^{ - 1}} $ 2. 根据式(24)构造加权矩阵$ {{\boldsymbol{W}}_{\text{s}}} $ 3. 初始化$ {\boldsymbol{\hat s}} = {\left( {{{\boldsymbol{H}}^{\text{H}}}{\boldsymbol{H}}} \right)^{ - 1}}{{\boldsymbol{H}}^{\text{H}}}{\boldsymbol{y}} $ 4. $ {\lambda _1} = \dfrac{1}{{{{\left\| {{\boldsymbol{y}} - {\boldsymbol{H\hat s}}} \right\|}_2}}} $ 5. 根据式(46)构造${{\boldsymbol{U}}_2}$ 6. $ {\boldsymbol{\hat s}} = {\lambda _1}{\left[ {{\lambda _1}{{\boldsymbol{H}}^{\text{H}}}{\boldsymbol{H}} + {M^{ - 1/2}}{\nabla ^{\text{H}}}{{\left( {{\boldsymbol{W}}_{\text{s}}^{1/2}} \right)}^{\text{H}}}{\boldsymbol{U}}_2^{\text{H}}{{\boldsymbol{U}}_2}{\boldsymbol{W}}_{\text{s}}^{1/2}\nabla } \right]^{ - 1}} $
${{\boldsymbol{H}}^{\text{H}}}{\boldsymbol{y}} $7. 重复迭代步骤4—步骤6，直至收敛 
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表 1 仿真参数
Table 1. Simulation parameters
参数 数值 载频 10 GHz 信号带宽 40 MHz 信号时宽 2 μs PRF 500 Hz 扫描速度 60 °/s 作用距离 3 km 波束宽度 3°
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表 2 机载雷达试验参数
Table 2. Experimental parameters for airborne radar
参数 数值 载频 30.75 GHz 信号时宽 1 μs 信号带宽 200 MHz PRF 4000 Hz俯仰角 ${20^ \circ }$ 波束宽度 ${4^ \circ }$ 扫描速度 $60\;{ ^ \circ }/{{\mathrm{s}}} $ 扫描范围 –30°～30° 平台速度 37 m/s 飞行高度 300 m
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表 3 试验结果图像熵对比
Table 3. Comparison of image Entropy for experimental results
超分辨方法 图像熵 LASSO-TV方法 2.7645 本文方法(SPICE-TV) 0.9721
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