Multi-task Learning of Sparse Autofocusing for High-Resolution SAR Imagery
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摘要: 针对传统高分辨合成孔径雷达(SAR)稀疏自聚焦成像算法难以有效平衡稀疏与聚焦特征的问题，该文提出一种基于交替方向多乘子方法(ADMM)的多任务协同优化学习稀疏自聚焦(MtL-SA)算法。该算法通过引入熵范数表征SAR成像结果聚焦特征，在ADMM优化框架下，利用近端算法求解聚焦特征解析解。针对原熵范数正则优化目标函数的非凸问题，该文合理设计代价函数，从而保证熵范数近端算子的闭合解析解。同时，应用
$ \ell {_1}$ 范数表征成像结果稀疏特征，并建立面向复数SAR成像数据的复数软阈值近端算子。该文所提MtL-SA成像算法可实现对目标场景后向散射场对应稀疏特征和聚焦特征的解析求解，并有效提升自聚焦算法的可靠性和稳健性。两种特征增强处理相互调和，保证了算法运行过程中有效降低误差传播，进而保证联合特征增强精度。仿真及实测机载SAR成像数据实验，验证了算法的有效性和实用性，同时应用相变分析方法分别定量和定性地分析了该文所提算法相比其他传统算法的优越性。Abstract: As it is difficult to balance the sparse and focusing features for conventional sparse autofocusing algorithm of Synthetic Aperture Radar (SAR), a Multi-task Learning Sparse Autofocusing (MtL-SA) algorithm is proposed under a novel Alternating Direction Method of Multipliers (ADMM) in this paper. The image entropy norm is introduced to model the focusing feature of the SAR imagery, and it is minimized in a regularized manner using the proximal algorithm. To overcome the non-convexity of the original objective function, a surrogate function under the ADMM framework is designed and optimized accordingly. This ensures closed-form solution of the errors and the focusing feature. Besides, the$ \ell {_1}$ -norm is applied to denote the intended sparse feature of the SAR imagery, and a complex-valued proximity operator is derived for the range-compressed SAR data. Due to the cooperative framework, both the features can be solved and achieved with high robustness and acceptable accuracy. Compared with conventions, the computational efficiency improved twice orders in terms of CPU time. The proposed MtL-SA algorithm can realize the analytical solutions of the sparse and focusing features, so as to improve the robustness of the joint enhancement. Experiments using airborne simulated and raw SAR data are performed to verify the effectiveness of the proposed algorithm. Phase transition analysis is applied to examine the superiority of the proposed algorithm compared with the conventions in terms of both quantitative and qualitative. -
表 1 MtL-SA算法流程
步骤1 设定初值${ {\boldsymbol{X} } }^{0}={ {\boldsymbol{Z} } }^{0}={ {\boldsymbol{D} } }^{0}={{{\textit{0}}} },\;k=0,\;G{=2}$，设定迭代停止准则，开始循环。 步骤2 全局优化：${\boldsymbol{X}}$更新运算${ {\boldsymbol{X} }^{k + 1} } = \left[ { { {\boldsymbol{A} }^{\rm{H} } }{ {\boldsymbol{E} }^{\rm{H} } }{\boldsymbol{Y} } + {\rho _1}\left( { { {\boldsymbol{Z} }_1}^k + { {\boldsymbol{D} }_1}^k} \right) + {\rho _2}\left( { { {\boldsymbol{Z} }_2}^k + { {\boldsymbol{D} }_2}^k} \right)} \right] \cdot {\left( { { {\boldsymbol{A} }^{\rm{H} } }{\boldsymbol{A} } + \rho G{\boldsymbol{I} } } \right)^{ - 1} }\quad \quad \quad \quad$ 步骤3 局部优化：${{\boldsymbol{Z}}_1}$, ${{\boldsymbol{D}}_1}$, ${{\boldsymbol{Z}}_2}$和${{\boldsymbol{D}}_2}$顺次更新运算 ${\rm{for }}\;\;g = G$ ${\boldsymbol{Z} }_{\rm{1} }^{k + 1} = {\left( { { {\boldsymbol{E} }^{k + 1} } } \right)^{\rm{H} } }{ {\boldsymbol{A} }^{\rm{H} } }{\boldsymbol{Y} },\;{\boldsymbol{D} }_{\rm{1} }^{k + 1} = {\boldsymbol{D} }_{\rm{1} }^k - { {\boldsymbol{X} }^{k + 1} } + {\boldsymbol{Z} }_{\rm{1} }^{k + 1}\quad \quad \quad \quad \quad$ ${\boldsymbol{Z} }_2^{k + 1} = {\rm{pro} }{ {\rm{x} }_{ { { {\lambda _2} } / \rho } } }\left[ { { {\boldsymbol{W} }^{k + 1} } } \right]{\rm{, } }{\boldsymbol{D} }_2^{k + 1} = {\boldsymbol{D} }_2^k - { {\boldsymbol{X} }^{k + 1} } + {\boldsymbol{Z} }_2^{k + 1}\quad \quad \quad \quad$ ${\rm{end}}$ ${{\boldsymbol{Z}}^{k + 1}} = \left[ {{\boldsymbol{Z}}_1^{k + 1}\;{\boldsymbol{Z}}_2^{k + 1}} \right],\;{{\boldsymbol{D}}^{k + 1}} = \left[ {{\boldsymbol{D}}_1^{k + 1}\;{\boldsymbol{D}}_2^{k + 1}} \right],\;k = k + 1$ 步骤4 当残差小于加性噪声方差时，跳至步骤5，迭代结束。否则，跳至步骤2。 步骤5 输出联合稀疏聚焦特征增强后的图像数据${\boldsymbol{X}}$。 
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