Geometry-Decoupled Deep Unfolding for Gridless Super-Resolution TomoSAR Under Nonuniform Baselines

Abstract

Super-resolution SAR tomography (TomoSAR) is performed on a discretized elevation grid, leading to off-grid bias and spectral leakage. Classical Toeplitz-Vandermonde gridless formulations avoid elevation discretization but rely on uniform sampling, whereas covariance- or subspace-based estimation is difficult in single-look repeat-pass TomoSAR. We propose DUSG-Tomo-Net, a geometry-decoupled deep unfolding framework for gridless inversion under nonuniform baselines. In DUSG-Tomo-Net, pairwise products of a single observation vector are related to a latent Toeplitz-compatible virtual-lag sequence through an analytical geometry operator and modeled as noisy covariance surrogates containing multi-scatterer cross terms, measurement noise, and lag-interpolation errors. Each unfolded layer combines learned lag-domain regularization, closed-form geometry-dependent data consistency, and finite-step Dykstra projection toward the set of Hermitian Toeplitz positive semidefinite matrices. Root-MUSIC then retrieves scatterer elevations in the continuous domain without an elevation dictionary. Because the trainable modules operate only on the common virtual-lag representation, the learned parameterization can be reused across representationally compatible acquisition geometries by recomputing the geometry operator. At 6 dB, simulations under nonuniform baselines yield a single-scatterer RMSE of 0.703 m and an effective detection rate of approximately 0.90 for two scatterers at the Rayleigh limit, while demonstrating reliable sub-Rayleigh separation. A model trained with 20 acquisitions remains applicable to perturbed configurations containing 8-28 acquisitions without retraining. Experiments on a 16-image CH-1 stack show that DUSG-Tomo-Net produces coherent urban elevation maps and more continuous double-scatterer structures than the gridless baseline method TADCG.