Off-Grid Differential Tomographic SAR and Its Application to Railway Monitoring

In conventional differential tomographic synthetic aperture radar (D-TomoSAR), the continuous elevation and linear velocity are usually discretized into a set of fixed grids and the scatterers are restricted to be on these predefined grids. The scatterers, however, do not necessarily lie on the prespecified grids. We propose an off-grid D-TomoSAR framework, in which the unknown parameters associated with the scatterers are continuously valued and the grid mismatch in traditional D-TomoSAR caused by discretization can be therefore overcome. Off-grid D-TomoSAR inversion is formulated as an $\ell _p$ ($0 \leq p \leq 1$) norm minimization problem with an unknown dictionary and an alternating descent-based iteratively reweighted least squares (IRLS) method, referred to as AD-IRLS, is proposed to solve the off-grid D-TomoSAR inversion. The algorithm alternately decreases the objective function and estimates the sparse signal and dictionary. Theoretical analysis is provided to verify AD-IRLS and the performance of the proposed approach is demonstrated by simulated and real data. Due to the great sensitivity of rails to subsidence deformation and the layover problem along railways, D-TomoSAR is extended to railway four-dimensional monitoring for the first time. Experimental results on railways and complex urban buildings, and comparisons between D-TomoSAR results and leveling measurements demonstrate the effectiveness of the proposed framework.