DUSG-Tomo-Net: A Deep Unfolded Neural Network for Super-Resolving Gridless Spaceborne SAR Tomography via Learned Toeplitz-Structured Covariance Representation

Synthetic aperture radar tomography (TomoSAR) enables 3-D imaging by exploiting multibaseline acquisitions and has become an important tool for urban mapping. To achieve super-resolution inversion, sparse reconstruction methods based on compressive sensing (CS) are widely adopted. However, most CS-based TomoSAR methods rely on grid-based formulations and therefore suffer from off-grid bias. Gridless formulations provide a principled way to alleviate this limitation, whereas classical Toeplitz-Vandermonde atomic norm minimization (ANM) is not directly applicable to spaceborne TomoSAR under nonuniform baselines. Existing gridless methods for nonuniform-baseline TomoSAR avoid the classical uniform linear array (ULA) assumption, but they are usually tightly coupled to handcrafted iterative solvers and solver-specific parameter settings, while robust inversion under limited observations and low-SNR conditions remains challenging. To address this gap, we propose DUSG-Tomo-Net, a deep unfolded gridless framework for single-look spaceborne TomoSAR under nonuniform baselines. The proposed method reformulates the inversion in a Toeplitz-compatible lag domain via a structured single-look approximation and recovers a Hermitian Toeplitz positive-semidefinite structured covariance representation through layerwise learned regularization and projection-based structural enforcement. The actual acquisition geometry is embedded analytically into the data-consistency step via a fixed, signal-independent operator, enabling operator-based adaptation to varying baseline configurations. Scatterer elevations are then estimated by a continuous-domain spectral estimator without elevation discretization.