Deep neural networks based on unrolled iterative algorithms have achieved remarkable success in sparse reconstruction applications, such as synthetic aperture radar (SAR) tomographic inversion (TomoSAR). However, the currently available deep learning-based TomoSAR algorithms are limited to 3-D reconstruction. The extension of deep learning-based algorithms to 4-D imaging, i.e., differential TomoSAR (D-TomoSAR) applications, is impeded mainly due to the high-dimensional weight matrices required by the network designed for D-TomoSAR inversion, which typically contain millions of freely trainable parameters. Learning such huge number of weights requires an enormous number of training samples, resulting in a large memory burden and excessive time consumption. To tackle this issue, we propose an efficient and accurate algorithm called HyperLISTA-ABT. The weights in HyperLISTA-ABT are determined in an analytical way according to a minimum coherence criterion, trimming the model down to an ultra-light one with only three hyperparameters. Additionally, HyperLISTA-ABT improves the global thresholding by utilizing an adaptive blockwise thresholding (ABT) scheme, which applies block-coordinate techniques and conducts thresholding in local blocks, so that weak expressions and local features can be retained in the shrinkage step layer by layer. Simulations were performed and demonstrated the effectiveness of our approach, showing that HyperLISTA-ABT achieves superior computational efficiency with no significant performance degradation compared to the state-of-the-art methods. Real data experiments showed that a high-quality 4-D point cloud could be reconstructed over a large area by the proposed HyperLISTA-ABT with affordable computational resources and in a fast time.

To achieve super-resolution synthetic aperture radar (SAR) tomography (TomoSAR), compressive sensing (CS)-based algorithms are usually employed, which are, however, computationally expensive, and thus is not often applied in large-scale processing. Recently, deep unfolding techniques have provided a good combination of physical model-based algorithms and the ability of neural networks to learn from data. In this vein, iterative CS-based algorithms can usually be un-rolled as neural networks with only 10 to 20 layers. When trained, it shows great computational efficiency for further TomoSAR processing. However, the learning architecture of neural networks built in this approach tends to result in error propagation and information loss, thus degrading the performance. In this paper, we propose to employ complex-valued sparse long short-term memory (CV-SLSTM) units to tackle this problem by incorporating historically updating information into the optimization procedure and preserving full information. Simulations are carried out to validate the performance of the proposed algorithm.

Finding sparse solutions of underdetermined linear systems commonly requires the solving ofL1regularized least squares minimization problem, which is also known as the basis pursuit denoising (BPDN). They are computationally expensive since they cannot be solved analytically. An emerging technique known asdeep unrollingprovided a good combination of the descriptive ability of neural networks, explainable, and computational efficiency for BPDN. Many unrolled neural networks for BPDN, e.g. learned iterative shrinkage thresholding algorithm and its variants, employ shrinkage functions to prune elements with small magnitude. Through experiments on synthetic aperture radar tomography (TomoSAR), we discover the shrinkage step leads to unavoidable information loss in the dynamics of networks and degrades the performance of the model. We propose a recurrent neural network (RNN) with novel sparse minimal gated units (SMGUs) to solve the information loss issue. The proposed RNN architecture with SMGUs benefits from incorporating historical information into optimization, and thus effectively preserves full information to the final output. Taking TomoSAR inversion as an example, extensive simulations demonstrated that the proposed RNN outperforms the state-of-the-art deep learning-based algorithm in terms of super-resolution power as well as generalization ability. It achieved 10% to 20% higher double scatterers detection rate and is less sensitive to phase and amplitude ratio difference between scatterers. Test on real TerraSAR-X spotlight images also shows high-quality 3-D reconstruction of test site.

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 article, we propose a novel deep learning-based super-resolving TomoSAR inversion approach,$\boldsymbol {\gamma }$-Net, to tackle this challenge.$\boldsymbol {\gamma }$-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$\boldsymbol {\gamma }$-Net approaches the Cramér-Rao lower bound (CRLB) while improving the computational efficiency by one to two 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,$\boldsymbol {\gamma }$-Net reaches more than 90% detection rate in moderate super-resolving cases at 25 measurements at 6 dB 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 TanDEM-X data with just six interferograms also shows high-quality 3-D reconstruction with high-density detected double scatterers.

Synthetic aperture radar tomography (TomoSAR) has been widely employed in 3-D urban mapping. However, state-of-the-art super-resolving TomoSAR algorithms are computationally expensive, because conventional numerical solvers need to solve the$l_{2^{-}}l_{1}$mix norm minimization. This paper proposes a computationally efficient super-resolving To-moSAR inversion algorithm based on deep learning. We studied the potential of deep learning to mimic a conventional$l_{2}-l_{1}$mix norm solver, i.e. iterative shrinkage thresholding algorithm (ISTA), and proposed several improvements of the complex-valued learned ISTA for TomoSAR inversion. Investigation on the super-resolution ability and estimator efficiency of the proposed algorithm shows that the proposed algorithm approaches the Cramer Rao lower bound (CRLB) with a computational efficiency more than 100 times better than the conventional solver.

SAR tomographic inversion (TomoSAR) has been widely employed for 3-D urban mapping. Existing algorithms are mostly based on an explicit inversion of the SAR imaging model, which are often computationally expensive for large scale processing. This is especially true for compressive sensing-based TomoSAR algorithms. Previous literature showed perspective of using data-driven methods like PCA and kernel PCA to decompose the signal and reduce the computational complexity of parameter inversion. This paper gives a preliminary demonstration of a data-driven TomoSAR method based on sparse Bayesian learning. Experiments on simulated data show the proposed algorithm can provide moderate detection rate and super-resolution power, comparing to the state-of-the-art compressive sensing based algorithms. As the proposed algorithm is purely based on conventional (non-superresolving) estimators, it is much more computationally efficient than compressive sensing based ones. This gives us a perspective of employing it for large scale TomoSAR processing. Experiments on real data will be given in the final paper.