基于稀疏分解的空间目标双基地ISAR自聚焦算法

空间目标双基地逆合成孔径雷达（ISAR）成像中，双基地角时变会造成二维图像的散焦。针对此问题，在三大同步理想可实现的条件下，以平稳空间目标为研究对象，分析了空间目标双基地ISAR成像原理，研究了双基地角时变对二维图像散焦的影响机理，提出了利用稀疏分解实现高精度自聚焦的算法。首先，将半双基地角的余弦进行泰勒展开；其次，结合目标的平动及转动条件，将成像相位项用多项式建模；然后，利用稀疏分解算法估计多项式的二次项系数，据此构建补偿项完成相位补偿。算法利用L-曲线准则选取正则参数，基于目标尺寸的先验信息构建冗余基的高分辨因子，利用推广的正则化欠定系统聚焦求解（FOCUSS）算法实现稀疏表示系数的估计，在恰当选取词典分辨率的条件下，算法可实现二次相位项的精确补偿，仿真实验验证了算法性能优于常用的非参数化自聚焦算法。

Algorithm for autofocusing of bistatic ISAR of space target based on sparse decomposition

In bistatic Inverse Synthetic Aperture Radar (ISAR) imaging of the space target, variation of the bistatic angle with time can cause defocusing of the two-dimensional image. To solve this problem, the principle for bistatic ISAR imaging of the stable space target is analyzed under the condition that the three synchronizations are realized ideally. The mechanism of influence of variation of the bistatic angle with time on defocusing of the two-dimensional image is researched, and an algorithm for autofocusing with high accuracy is proposed based on sparse decomposition. The cosine of half of the bistatic angel is approximated with Taylor expansion, and then the imaging phase is modelized as a polynomial according to the translation and rotation conditions of the space target. The second-order coefficient of the polynomial is obtained based on the sparse decomposition algorithm, and the compensation item is constructed to complete phase compensation with the obtained coefficient. Regular parameters are determined according to the L-curve criterion. High resolution factors of the redundant basis is designed based on prior information of the target size. Sparse representation coefficients are estimated with the extended generalization FOCal Underdetermined System Solver (FOCUSS) algorithm. The second-order phase item can be compensated accurately if the redundant dictionary resolution is chosen appropriately. The simulation experiment proves that performance of the algorithm proposed is prior to that of the common algorithm for non-parameter autofocusing.