L₁ Minimization with Perturbation for Off-grid Tomographic SAR Imaging

Synthetic Aperture Radar (SAR) Tomography (TomoSAR) is a novel technique that enables three-Dimensional (3-D) imaging using multi-baseline two-Dimensional (2-D) data. The essence of TomoSAR is actually to solve a one-dimensional spectral estimation problem. Compressed Sensing-based (CS) algorithm can retrieve solutions with only a few non-uniform acquisitions and has gradually become the main imaging method. In the conventional processing flow of CS algorithms, the continuous elevation direction is divided into a pre-set grid, and the targets are assumed to be exactly on the grid. ${{L}}_{1}$ minimization has been proven to be effective in TomoSAR imaging. In the conventional processing flow, the continuous elevation axis is divided into fixed grids, and scatters are assumed to be exactly on the pre-set grid. However, this hypothesis is generally untenable, and will lead to a problem called “Basis Mismatch”, which is rarely discussed in TomoSAR. In this letter, we first discuss the model of Off-grid TomoSAR, and then propose an addictive perturbation model to compensate for the errors caused by the grid effect. We utilize the local optimization thresholding algorithm to solve the complex-valued ${{L}}_{1}$ minimization problem of TomoSAR. We conducted experiments both on simulation data and actual airborne flight data. Our simulation results indicate that the proposed method can estimate a more accurate position of scatters, which leads to better original signal recovery. The reconstruction results of actual data verify that the impact of grid mismatch can be mostly eliminated.