Feature Reconstruction of High Resolution SAR Imagery Based on Low Rank Matrix Completion
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摘要: 在对抗电磁环境中，机载合成孔径雷达(SAR)容易受到电子干扰，造成若干回波脉冲不可用，导致SAR回波部分数据丢失，成像性能受限。由此，该文提出了一种基于低秩矩阵补全的特征重建SAR(FR-SAR)成像算法。考虑到SAR回波数据的低秩特性，引入矩阵分解获取行或列的非零数，应用因式组稀疏正则化(FGSR)算法对非零列数取凸优化，可获取SAR回波数据之间的相关性，从而实现SAR回波数据的补全。同时为了提升该算法的抑噪声性能和高分辨能力，将稀疏先验引入正则化模型。利用交替方向多乘子法(ADMM)实现矩阵补全和稀疏特征增强协同求解。FR-SAR算法由于未使用奇异值分解(SVD)，运算效率更高。仿真和实测实验验证了FR-SAR算法的有效性，同时利用相变分析方法(PTD)对所提算法和传统算法的恢复能力进行定量对比，均验证了FR-SAR算法的优越性。Abstract: In a countermeasure electromagnetic environment, airborne Synthetic Aperture Radar (SAR) is prone to electronic interference, which makes some echo pulses unavailable, resulting in partial data loss of the SAR echo and limited imaging performance. Thus, a Feature Reconstruction SAR (FR-SAR) imaging algorithm based on low-rank matrix completion is proposed. By considering the low-rank characteristics of the echoed data, the nonzero column number of rows or columns is obtained through matrix decomposition, and the nonzero column number is convexly optimized by Factor Group-Sparse Regularization (FGSR) to obtain the correlation between SAR echoes, to achieve data completion. Additionally, the proposed algorithm in the rank function is more accurate than the conventional nuclear function. Meanwhile, a sparse prior is introduced into the regularization model to improve the noise suppression and super-resolution performance. The Alternating Direction Method of Multipliers (ADMM) is used to realize a collaborative solution between matrix completion and sparse feature enhancement. The FR-SAR algorithm is more efficient because it does not use Singular Value Decomposition (SVD). Simulated and measured data verify the effectiveness of the FR-SAR algorithm. The recovery abilities of the proposed and traditional algorithms are quantitatively compared using a Phase Transition Diagram (PTD), establishing the superiority of the FR-SAR algorithm.
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