一种快速复数线性Bregman迭代算法及其在ISAR成像中的应用

A fast complex linearized Bregman iteration algorithm and its application in ISAR imaging

为实现具有任意稀疏结构的多量测向量(multiple measurement vectors,MMV)问题的快速重构.本文提出一种快速复数线性Bregman迭代算法(fast complex linearized Bregman iteration algorithm,FCLBI)并将其应用于逆合成孔径雷达(inverse synthetic aperture radar,ISAR)成像.首先,构建了任意稀疏结构的MMV信号模型并分析了其信号特征;其次,推导了复数条件下FCLBI算法的迭代公式用于重构MMV问题,将算法拓展到复数域使其更具普适性;然后,通过估计Bregman迭代过程中的停滞步长与感知矩阵优化相结合的方式减少迭代次数,从而可加快运算速度;最后,将算法应用于ISAR成像,进一步提高了稀疏恢复理论用于ISAR成像时的速度和抗噪性能.仿真和实测数据实验验证了算法的有效性.

To implement fast reconstruction of the multiple measurement vectors （MMV） problem under arbitrary sparse structures, a fast complex linearized Bregman iteration （FCLBI） algorithm is proposed and applied to inverse synthetic aperture radar （ISAR） imaging. First, a signal model of an arbitrary sparse structure is established and its signature is analyzed. Second, an iterative formula for the FCLDI algorithm is deduced in a complex domain to recover the signals of the arbitrary sparse structure, thus extending its universality for complex-valued data. Third, by combining stagnation step estimation and sensing matrix optimization, the total iterative numbers are decreased to improve computational efficiency. Finally, the algorithm is applied to ISAR imaging, which reduces imaging time. Simulations and experiments with real-world data show the effectiveness and robustness of the proposed algorithm.