基于半正定规划的压缩感知线阵三维SAR自聚焦成像算法

线阵合成孔径雷达(Linear Array Synthetic Aperture Radar, LASAR)3维成像技术是一种具有重要潜在应用价值的新体制成像雷达，压缩感知稀疏重构是近几年实现LASAR高分辨3维成像的热点研究之一。但相对于传统2维SAR，受线阵稀疏分布及阵列-平台2维联动，压缩感知LASAR成像面临回波数据欠采样、多维度高阶相位误差等问题，传统SAR自聚焦算法难以适用于压缩感知LASAR 3维稀疏自聚焦成像。为克服欠采样条件下多维度高阶相位误差对LASAR成像的影响，该文提出了一种基于半正定规划的压缩感知LASAR自聚焦成像算法。首先，结合压缩感知成像理论、图像最大锐度及最小均方误差准则，构造欠采样条件下稀疏目标的相位误差估计模型；其次，利用松弛半正定规划方法估计相位误差；最后，利用迭代逼近方法提高相位误差估计精度，实现压缩感知LASAR高精度稀疏自聚焦成像。另外，通过主散射目标区域提取，仅采用主散射区域进行相位误差估计，进一步提高自聚焦算法运算效率。仿真数据和实测数据验证了该文算法的有效性。 

Compressed Sensing Linear Array SAR Autofocusing Imaging via Semi-definite Programming

Linear Array Synthetic Aperture Radar (LASAR) is a novel and promising radar imaging technique. In recent years, Compressed Sensing (CS) sparse recovery has been a research focus for high-resolution three-Dimensional (3-D) LASAR imaging. Compared with the traditional two-Dimensional (2-D) SAR imaging, LASAR suffers from many problems, including under-sampling data and multi-dimensional and higher-order phase errors due to its sparse Linear Array Antenna (LAA) and the joint 2-D motions of the platform and LAA. The conventional autofocusing methods of 2-D SAR may be not suitable for CS-based LASAR 3-D sparse autofocusing. To address the multi-dimensional and higher-order phase errors in LASAR 3-D imaging with respect to under-sampling data, in this paper, we propose a sparse autofocusing algorithm based on semi-definite programming for CS-based LASAR imaging. First, by combining CS-based imaging theory, image maximum sharpness, and the minimum square error principle, we construct a LASAR phase-error estimation model based on under-sampled data. Next, we use semi-definite programming relaxation to estimate the phase errors. Lastly, we employ an iterated approximation method to improve the precision of the phase-error estimation and achieve the final CS-based LASAR autofocusing. To further improve the efficiency of the algorithm, we select only the dominant scattering areas for LASAR phase-error estimation. We present our simulation and experimental results to confirm the effectiveness of out proposed algorithm.