Efficient ADMM Algorithm for Atomic Norm Minimization in SAR Tomography

The atomic norm minimization (ANM) method has been well-applied in tomographic synthetic aperture radar (TomoSAR) inversion, which can provide accurate scatterer localization and eliminate the outliers effectively. In order to solve the ANM, it is usually converted into a semidefinite programming (SDP) problem. However, this second-order optimization problem suffers from high computational cost when searching for the optimal solution. Since TomoSAR often faces large-scale processing of urban scenes, improving the computational efficiency will benefit greatly. In this article, we develop and derive an efficient alternating direction method of multipliers (ADMM) implementation for the ANM method to solve the TomoSAR inversion problem, which is named as the ANM-ADMM algorithm. The detection performance, estimation accuracy, and computational efficiency of the proposed ANM-ADMM algorithm have been carefully analyzed by both simulation and real TerraSAR-X experiments. By comparing with the original ANM-SDP algorithm, it is clear that the ANM-ADMM algorithm can acquire considerable estimation accuracy and can meanwhile improve the computational efficiency significantly.