Enhanced Matrix Completion Method for Super-resolution Tomography SAR Imaging: First Large-scale Urban 3-D High-resolution Results of LT-1 Satellites Using Monostatic Data

LuTan-1 (LT-1) constellation is an innovative distributed L-band spaceborne synthetic aperture radar (SAR), which can potentially provide tomographic mapping with twin satellites, i.e., Tomographic SAR (TomoSAR) imaging. Usually, compressed sensing (CS) techniques can be used in TomoSAR imaging to improve the elevation resolution by exploiting the layout sparsity. However, the off-grid effect of discrete dictionary used in traditional CS methods tends to dramatically degrade the imaging performance. In this paper, a novel non-convex enhanced matrix completion (NcEMC) algorithm is proposed for gridless super-resolution TomoSAR imaging. Specifically, a Hankel matrix completion model is firstly designed to effectively exploit the latent data structure in an off-grid manner. Benefiting from the enhanced low-rankness of Hankel matrix form, a more refined uniform baseline observation is reconstructed from the original configuration using the optimization of matrix completion with the achievement of signal enhancement. To avoid using a regularization term to balance the traditional singular value decomposition solution of Hankel matrix, the proposed algorithm restates the low-rank constraint in a symmetric decomposition manner, which is beneficial to reduce the computation cost. Subsequently, an incoherence condition is introduced as a significant constraint in the non-convex Hankel matrix reconstruction process. To this end, a projected gradient descent iteration method is designed to satisfy the incoherence condition, thereby facilitating a more robust and accurate process of data reconstruction. Meanwhile, this paper presents the first large-scale urban 3-D high-resolution results of LT-1 satellites. We use a collection of 10 repeat-pass LT-1 monostatic SAR images to demonstrate the entire processing in tomographic SAR imaging application and the superiority of the proposed algorithm.