A Two-Step Dual-Polarimetric Sparse Bayesian Learning D-TomoSAR Method for Urban Building Deformation Monitoring

SAR tomography (TomoSAR) is capable of separating scatterers at different elevations within the same range–azimuth resolution cell. Differential TomoSAR (D-TomoSAR) further incorporates temporal information, enabling joint estimation of scatterer elevation and deformation velocity. Most existing sparse inversion methods rely on single-polarization observations, and the joint use of observations across polarization channels remains limited. Separating adjacent and weak scatterers in complex urban layover scenarios remains challenging. Sparse Bayesian learning (SBL) offers strong capabilities for sparse support recovery and super-resolution parameter estimation. When SBL is applied over a global fine grid in the two-dimensional elevation–deformation parameter space, the high correlation among neighboring dictionary atoms may hinder the separation of adjacent scatterers and affect the stability of sparse support recovery. To address these issues, this paper proposes a two-step sparse Bayesian learning (TSSBL) D-TomoSAR method with a dual-polarization shared-support constraint. First, joint Orthogonal Matching Pursuit (OMP) search is performed on a coarse grid using HH/VV observations to achieve global coarse localization of potential scatterers. Subsequently, a local fine grid is constructed around the candidate positions, and SBL is performed under an HH/VV shared-support constraint to achieve refined estimation of scatterer elevation and linear deformation velocity. Finally, the number of effective scatterers is determined through a statistical test based on residual reduction. Simulation and real-data experiments demonstrate favorable scatterer separation and joint elevation–deformation estimation performance. Using 22 PAZ HH/VV images, the proposed Dual-Pol TSSBL method achieves a building-height root-mean-square error (RMSE) of 2.72 m for five buildings with reference heights. The results indicate that combining dual-polarization shared support with coarse-to-fine SBL inversion can effectively improve joint elevation–deformation estimation for urban buildings in D-TomoSAR under limited observations, with potential for future application to large-scale urban building deformation monitoring using long SAR time series.