Toeplitz-structured deep unfolding network for TomoSAR 3-D reconstruction

Urban area 3-D imaging is a key application of synthetic aperture radar (SAR). Classical compressive sensing-based tomographic SAR methods rely on iterative optimization, which is computationally expensive and sensitive to hyperparameter tuning, limiting its scalability for large scenes. Deep unfolding networks offer a promising alternative but still suffer from inaccurate estimation of target elevations and amplitudes. Therefore, this paper proposes the Toeplitz-structured learned iterative shrinkage–thresholding algorithm with an adaptive elevation target determination module (Toe-LISTA-Ada) for efficient and accurate TomoSAR 3-D reconstruction. First, complex-valued operators are employed to directly process SAR measurements, ensuring the preservation of phase information. Then, by exploiting the Toeplitz structure of the Gram matrix of the TomoSAR observation model, Toe-LISTA-Ada replaces explicit matrix multiplication with a convolutional operation, significantly reducing the number of trainable parameters while retaining physical consistency, thereby accelerating convergence and improving reconstruction accuracy. Finally, an adaptive elevation target determination module is incorporated to account for the limited number of dominant scatterers along the elevation direction in urban scenes, enhancing target separability and elevation estimation performance under severe layover and noise conditions. The proposed network is trained on simulated data that are consistent with real imaging parameters and evaluated on measured datasets. Experimental results demonstrate that Toe-LISTA-Ada achieves improved accuracy in both elevation target localization and amplitude estimation, while exhibiting a capability for 3-D point cloud denoising. The source code is publicly available at: https://github.com/ormosia6/TomoSAR-Toe-LISTA .