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, γ-Net, to tackle this
challenge. γ-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 γ-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,
γ-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