Fast Split Bregman Based Deconvolution Algorithm for Airborne Radar Imaging

Abstract

Deconvolution methods can be used to improve the azimuth resolution in airborne radar imaging. Due to the sparsity of targets in airborne radar imaging, an L 1 regularization problem usually needs to be solved. Recently, the Split Bregman algorithm (SBA) has been widely used to solve L 1 regularization problems. However, due to the high computational complexity of matrix inversion, the efficiency of the traditional SBA is low, which seriously restricts its real-time performance in airborne radar imaging. To overcome this disadvantage, a fast split Bregman algorithm (FSBA) is proposed in this paper to achieve real-time imaging with an airborne radar. Firstly, under the regularization framework, the problem of azimuth resolution improvement can be converted into an L 1 regularization problem. Then, the L 1 regularization problem can be solved with the proposed FSBA. By utilizing the low displacement rank features of Toeplitz matrix, the proposed FSBA is able to realize fast matrix inversion by using a Gohberg–Semencul (GS) representation. Through simulated and real data processing experiments, we prove that the proposed FSBA significantly improves the resolution, compared with the Wiener filtering (WF), truncated singular value decomposition (TSVD), Tikhonov regularization (REGU), Richardson–Lucy (RL), iterative adaptive approach (IAA) algorithms. The computational advantage of FSBA increases with the increase of echo dimension. Its computational efficiency is 51 times and 77 times of the traditional SBA, respectively, for echoes with dimensions of 218 × 400 and 400 × 400 , optimizing both the image quality and computing time. In addition, for a specific hardware platform, the proposed FSBA can process echo of greater dimensions than traditional SBA. Furthermore, the proposed FSBA causes little performance degradation, when compared with the traditional SBA.

A Superfast Super-Resolution Method for Radar Forward-Looking Imaging

“…Sparse regularization is an effective method for improving the azimuth resolution because the target of interest is usually sparse in radar forward-looking imaging. In the previous work, we conducted in-depth research on sparse regularization methods [ 18 , 19 ]. Typically, the sparse regularization method requires solving an regularization problem [ 20 , 21 ].…”

“…In radar imaging, the echo dimension is usually large, and the existence of inversion seriously restricts the calculation efficiency. In our recent study, the high computational complexity of matrix inversion has been decreased by the Gohberg-Semencul (GS) representation [ 19 ] (We named it FSBA in [ 19 ]), which reduces the computational complexity of each iteration from to ; however, it usually takes hundreds of iterations to converge to the optimal solution. In practical applications, we need the radar to provide clear target information in the imaging area in real time, which confers high requirements for the real-time performance of the radar.…”

Superresolution of Radar Forward-Looking Imaging Based on Accelerated TV-Sparse Method

“…According to Rayleigh criterion, targets with a distance smaller than the Rayleigh distance (RD) are located at the same resolution cell and cannot be distinguished separately, where RD is the space between the peak of the antenna pattern and the first zero-crossing [5][6][7]. This shows that the resolution of real aperture imaging cannot beyond one beam width.…”

“…In [28], T. Kailath proposed the concepts of displacement structure and displacement rank, as well as revealing that the operation can be compressed by using a Toeplitz matrix. It has been proven that the displacement rank of a Toeplitz matrix is very small and, so, its inverse matrix also has a displacement structure, which laid the theoretical foundation for the fast solution of Toeplitz equations [29,30]. Recently, utilizing the low displacement rank features of Toeplitz matrices, along with the Gohberg-Semencul (GS) representation, the fast inversion of Toeplitz matrices has been studied [31].…”

Fast Total Variation Method Based on Iterative Reweighted Norm for Airborne Scanning Radar Super-Resolution Imaging

“…Airborne scanning radar works as a noncoherent sensor and realizes forward-looking area imaging by sweeping the observation scenarios. This imaging system is widely used in the fields of ground mapping, microwave radiometers remote sensing, autonomous landing and self-driveless [1][2][3][4][5]. High range resolution can be obtained by emitting the large time-bandwidth product signal such as linear frequency modulation (LFM) signal and an impulse compression technique.…”