DLSLA 3-D SAR imaging algorithm for off-grid targets based on pseudo-polar formatting and atomic norm minimization

Abstract

This paper concerns the imaging problem for downward looking sparse linear array three-dimensional synthetic aperture radar (DLSLA 3-D SAR) under the circumstance of sparse and non-uniform cross-track dimensional virtual phase centers configuration. Since the 3-D imaging scene behaves typical sparsity in a certain domain, sparse recovery approaches hold the potential to achieve a better reconstruction performance. However, most of the existing compressive sensing (CS) algorithms assume the scatterers located on the pre-discretized grids, which is often violated by the off-grid effect. By contrast, atomic norm minimization (ANM) deals with sparse recovery problem directly on continuous space instead of discrete grids. This paper firstly analyzes the off-grid effect in DLSLA 3-D SAR sparse image reconstruction, and then introduces an imaging method applied to off-gird targets reconstruction which combines 3-D pseudo-polar formatting algorithm (pseudo-PFA) with ANM. With the proposed method, wave propagation and along-track image reconstruction are operated with pseudo-PFA, then the cross-track reconstruction is implemented with semidefinite programming (SDP) based on the ANM model. The proposed method holds the advantage of avoiding the off-grid effect and managing to locate the off-grid targets to accurate locations in different imaging scenes. The performance of the proposed method is verified and evaluated by the 3-D image reconstruction of different scenes, i.e., point targets and distributed scene.

创新点

下视稀疏线性阵列三维合成孔径雷达(DLSLA 3-D SAR)常常由于跨航向的稀疏阵列安装条件受限等因素出现等效相位中心缺失和非均匀分布的情况,造成跨航向稀疏非均匀采样。对于具有稀疏性的3-D SAR成像场景,压缩感知(CS)方法能够在稀疏非均匀采样情况下获得良好的重构效果。然而,大多数CS算法都是基于离散假设,即假设散射点准确位于离散网格上;当真实散射点与离散网格不重合时,CS算法的重构效果将会受到网格偏离现象(off-grid effect)的影响。与离散的CS算法不同,原子范数最小化方法(ANM)直接在连续域上对稀疏信号进行恢复,不受网格偏离现象的影响。本文首先分析了DLSLA 3-D SAR跨航向稀疏重构时存在的网格偏离现象,然后提出了伪极坐标变换与原子范数最小化结合的成像算法。该算法首先通过距离压缩对波传播方向成像,然后对航迹向和跨航向进行伪极坐标变换,并通过傅里叶变换实现航迹向成像,然后在跨航向利用原子范数最小化方法进行成像。本文提出的方法能够在不同的成像场景中避免网格偏离现象、获得精确的成像结果。不同成像场景(点目标和分布式目标场景)的仿真实验成像结果验证了本文算法的有效性。