Structured Low-rankness Method of Joint Neighboring Pixels for Tomographic SAR 3D Imaging

Tomographic SAR (TomoSAR) has significant value in scientific research and applications, as it enables three-dimensional (3D) imaging to address limitations such as scene overlay and projection geometric distortion. The elevation resolution of TomoSAR is limited by the aperture in the elevation direction. Consequently, super-resolution algorithms such as Compressive Sensing (CS) are generally used to enhance the performance of 3D imaging. However, conventional CS methods suffer from grid mismatch issues due to predefined discrete grids, which lead to limited resolution under practical constraints, such as limited channels and low signal-to-noise ratios. To address these limitations, a novel, gridless, super-resolution algorithm based on the structured low-rankness of joint neighboring pixels is proposed herein for tomographic 3D SAR Imaging. By enhancing the intrinsic structural observation, the efficacy of the model for 3D reconstruction can be effectively improved by increasing the number of valid observations. Specifically, a gridless, structured, low-rank, non-convex optimization model is constructed by leveraging the joint sparse characteristics of neighboring pixels, overcoming the limitations of traditional sparse grid-based approaches. Furthermore, an efficient solution is achieved using a projected gradient descent algorithm, and the dependence of the reconstruction performance on the sampling positions is reduced by introducing an incoherent feasible region constraint. Finally, the superiority of the proposed algorithm is validated through both simulation and analysis of real measured datasets, including the SARMV3D-1.0 airborne array dataset and spaceborne LuTan-1 dataset. The proposed algorithm achieves superior 3D reconstruction accuracy and stability compared to most existing state-of-the-art methods.