一种基于勒让德拟合的SAR 后向投影自聚焦算法

对于合成孔径雷达(SAR)成像来说，后向投影(Back Projection, BP)算法是一种十分重要的时域成像方法。然而现有的自聚焦算法都是基于频域成像算法开发的，无法直接用于BP 聚焦图像的误差相位估计。针对这一问题，该文提出一种适用于BP 图像的自聚焦算法。该算法以图像锐度函数为目标函数，以待估计的相位校正值为自变量，通过坐标下降最优化算法循环迭代获得它们的最优估计。在问题求解中，该算法利用勒让德多项式来拟合目标函数，使得每次迭代的最优解可以解析地获得，避免了低效的线搜索过程。基于仿真数据和实测数据的实验验证了该算法的精确性和有效性。 

A SAR Back Projection Autofocusing Algorithm Based on Legendre Approximation

The Back Projection (BP) algorithm is a very important time-domain methodology for Synthetic Aperture Radar (SAR) imaging. However, conventional autofocus techniques are based on frequency-domain imaging algorithms, and can not be directly applied to BP imagery for error phase estimation. In this paper, an autofocus algorithm for BP imagery is proposed. The algorithm takes image sharpness as an objective function, and employs the coordinate descent optimization scheme to obtain the optimum phase-corrected variables by iterations. In the implementation, with a Legendre approximation of the objective function, the optimal phase estimation can be found analytically for each parameter within an iteration, avoiding computationally expensive line-search procedures. The experimental results with both simulated and measured data confirm the accuracy and effectiveness of the proposed algorithm.