Huo Weibo, Zhang Qiping, Zhang Yin, Zhang Yongchao, Huang Yulin, Yang Jianyu
School of Information and Communication Engineering, University of Electronic Science and Technology of China, No. 2006, Xiyuan Ave, West Hi-Tech Zone, Chengdu 611731, China.
Sensors (Basel). 2021 Jan 26;21(3):817. doi: 10.3390/s21030817.
The super-resolution method has been widely used for improving azimuth resolution for radar forward-looking imaging. Typically, it can be achieved by solving an undifferentiable L1 regularization problem. The split Bregman algorithm (SBA) is a great tool for solving this undifferentiable problem. However, its real-time imaging ability is limited to matrix inversion and iterations. Although previous studies have used the special structure of the coefficient matrix to reduce the computational complexity of each iteration, the real-time performance is still limited due to the need for hundreds of iterations. In this paper, a superfast SBA (SFSBA) is proposed to overcome this shortcoming. Firstly, the super-resolution problem is transmitted into an L1 regularization problem in the framework of regularization. Then, the proposed SFSBA is used to solve the nondifferentiable L1 regularization problem. Different from the traditional SBA, the proposed SFSBA utilizes the low displacement rank features of Toplitz matrix, along with the Gohberg-Semencul (GS) representation to realize fast inversion of the coefficient matrix, reducing the computational complexity of each iteration from O(N3) to O(N2). It uses a two-order vector extrapolation strategy to reduce the number of iterations. The convergence speed is increased by about 8 times. Finally, the simulation and real data processing results demonstrate that the proposed SFSBA can effectively improve the azimuth resolution of radar forward-looking imaging, and its performance is only slightly lower compared to traditional SBA. The hardware test shows that the computational efficiency of the proposed SFSBA is much higher than that of other traditional super-resolution methods, which would meet the real-time requirements in practice.
超分辨率方法已被广泛用于提高雷达前视成像的方位分辨率。通常，它可以通过解决一个不可微的L1正则化问题来实现。分裂Bregman算法（SBA）是解决这个不可微问题的一个很好的工具。然而，其实时成像能力受限于矩阵求逆和迭代。尽管先前的研究利用系数矩阵的特殊结构来降低每次迭代的计算复杂度，但由于需要数百次迭代，其实时性能仍然有限。本文提出了一种超快速SBA（SFSBA）来克服这一缺点。首先，在正则化框架下将超分辨率问题转化为L1正则化问题。然后，使用所提出的SFSBA来解决不可微的L1正则化问题。与传统SBA不同之处在于，所提出的SFSBA利用托普利兹矩阵的低位移秩特征，结合戈伯格 - 塞门库尔（GS）表示来实现系数矩阵的快速求逆，将每次迭代的计算复杂度从O(N3)降低到O(N2)。它采用二阶向量外推策略来减少迭代次数。收敛速度提高了约8倍。最后，仿真和实际数据处理结果表明，所提出的SFSBA能够有效提高雷达前视成像的方位分辨率，其性能与传统SBA相比仅略低。硬件测试表明，所提出的SFSBA的计算效率远高于其他传统超分辨率方法，能够满足实际中的实时要求。
