# boldsymbolγ-Net: Superresolving SAR Tomographic Inversion via Deep Learning

arXiv: https://arxiv.org/abs/2112.04211 · HTML: https://mlsanity.com/paper/2112.04211/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Dec 2021.

## Built on by (most cited first, 5 of 5)

- [A Deep Learning Approach for SAR Tomographic Imaging of Forested Areas](https://mlsanity.com/paper/2301.08605/) (2023)
- [ATASI-Net: An Efficient Sparse Reconstruction Network for Tomographic SAR Imaging with Adaptive Threshold](https://mlsanity.com/paper/2211.16855/) (2022)
- [Reconstructing Building Height from Spaceborne TomoSAR Point Clouds Using a Dual-Topology Network](https://mlsanity.com/paper/2601.00658/) (2026)
- [Solving 3D Radar Imaging Inverse Problems with a Multi-cognition Task-oriented Framework](https://mlsanity.com/paper/2211.14989/) (2022)
- [A Model-data-driven Network Embedding Multidimensional Features for Tomographic SAR Imaging](https://mlsanity.com/paper/2211.15002/) (2022)

## Abstract (arXiv)

Synthetic aperture radar tomography (TomoSAR) has been extensively employed in 3-D reconstruction in dense urban areas using high-resolution SAR acquisitions. Compressive sensing (CS)-based algorithms are generally considered as the state of the art in super-resolving TomoSAR, in particular in the single look case. This superior performance comes at the cost of extra computational burdens, because of the sparse reconstruction, which cannot be solved analytically and we need to employ computationally expensive iterative solvers. In this paper, we propose a novel deep learning-based super-resolving TomoSAR inversion approach, boldsymbolγ-Net, to tackle this challenge. boldsymbolγ-Net adopts advanced complex-valued learned iterative shrinkage thresholding algorithm (CV-LISTA) to mimic the iterative optimization step in sparse reconstruction. Simulations show the height estimate from a well-trained boldsymbolγ-Net approaches the Cram'er-Rao lower bound while improving the computational efficiency by 1 to 2 orders of magnitude comparing to the first-order CS-based methods. It also shows no degradation in the super-resolution power comparing to the state-of-the-art second-order TomoSAR solvers, which are much more computationally expensive than the first-order methods. Specifically, boldsymbolγ-Net reaches more than 90% detection rate in moderate super-resolving cases at 25 measurements at 6dB SNR. Moreover, simulation at limited baselines demonstrates that the proposed algorithm outperforms the second-order CS-based method by a fair margin. Test on real TerraSAR-X data with just 6 interferograms also shows high-quality 3-D reconstruction with high-density detected double scatterers.