One Dimensional High Resolution Range Imaging Method of Stepped Frequency ISAR Based on Atomic Norm Minimization
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摘要: 针对传统离散化压缩感知方法在网格失配条件下步进频率(SF) ISAR 1维距离成像估计性能下降的问题，该文提出一种基于原子范数最小化(ANM)的高分辨距离成像方法。首先，构建基于原子范数的无网格SF ISAR距离向稀疏表示模型，将1维距离成像问题转化为原子系数以及频率估计问题。然后，利用原子范数半正定性质，将原子范数最小化问题转化为半正定规划问题，并基于交替方向乘子法实现快速求解。最后，利用Vandermonde分解得到最终的1维高分辨距离成像结果。由于避免了网格离散化处理，因此可以实现网格失配、低量测值条件下的高分辨距离成像，且保持了高的距离分辨能力。理论分析与仿真实验验证了所提方法的有效性。Abstract: In order to solve the problem that the performance of one-dimensional range profile synthesis performance of Stepped Frequency (SF) ISAR based on the traditional discrete compressed sensing method declines under the condition of off-grid, a high-resolution range profile synthesis method of SF ISAR based on Atomic Norm Minimization (ANM) is proposed. Firstly, a grid free SF ISAR range sparse representation model based on atomic norm is constructed, and the one-dimensional range synthesis problem is transformed into the atomic coefficient and frequency estimation problem. Then, the atomic norm minimization problem is transformed into a semi-positive definite programming problem by using the semi-positive definite property of the atomic norm, and the fast solvers are performed via the alternating direction method of multipliers. Finally, the final one-dimensional high-resolution range profile imaging results are obtained by Vandermonde decomposition. Because the grid discretization is avoided, the high-resolution range profile imaging can be realized under the condition of grid mismatch and low measurement, and the high range resolution can be maintained. Theoretical analysis and simulation experiments verify the effectiveness of the proposed method.
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