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.
Highlights
High-resolution airborne radar imagery are beneficial for obtaining accurate target information of imaging regions in many applications in the military and civilian fields, such as precise guidance of weapons, autonomous landing of aircraft, topographic mapping, and so on
Many methods have been presented to relax the ill-posedness of deconvolution, such as Wiener filtering (WF) [7], truncated singular value decomposition (TSVD) [8], Tikhonov regularization (REGU) [9], Richardson–Lucy (RL) [10], iterative adaptive approach (IAA) [11], and so on, they have only achieved limited resolution improvement in airborne radar imaging
We proposed the fast split Bregman algorithm (FSBA) to solve the problem of low azimuth resolution in airborne radar imaging
Summary
High-resolution airborne radar imagery are beneficial for obtaining accurate target information of imaging regions in many applications in the military and civilian fields, such as precise guidance of weapons, autonomous landing of aircraft, topographic mapping, and so on. The split Bregman algorithm (SBA) has been widely utilized to solve the non-differentiable L1 regularization problem, obtaining good effect in many fields such as optical imaging [17,18], radar imaging [19,20], compressed sensing [21,22], computed tomography (CT) [23,24], magnetic resonance imaging (MRI) [21,25], and so on In this process, it is necessary to invert a coefficient matrix, resulting in high computational costs due to the computational complexity of matrix inversion, which is O(N3).
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