Synthetic aperture radar tomography (TomoSAR) is an important 3D mapping method. Traditional TomoSAR requires a large number of observation orbits however, it is hard to meet the requirement of massive orbits. While on the one hand, this is due to funding constraints, on the other hand, because the target scene is changing over time and each observation orbit consumes lots of time, the number of orbits can be fewer as required within a narrow time window. When the number of observation orbits is insufficient, the signal-to-noise ratio (SNR), peak-to-sidelobe ratio (PSR), and resolution of 3D reconstruction results will decline severely, which seriously limits the practical application of TomoSAR. In order to solve this problem, we propose to use a deep learning network to improve the resolution and SNR of 3D reconstruction results under the condition of very few observation orbits by learning the prior distribution of targets. We use all available orbits to reconstruct a high resolution target, while only very few (around 3) orbits to reconstruct a low resolution input. The low-res and high-res 3D voxel-grid pairs are used to train a 3D super-resolution (SR) CNN (convolutional neural network) model, just like ordinary 2D image SR tasks. Experiments on the Civilian Vehicle Radar dataset show that the proposed deep learning algorithm can effectively improve the reconstruction both in quality and in quantity. In addition, the model also shows good generalization performance for targets not shown in the training set.

SAR tomography (TomoSAR) is an important technology for three-dimensional (3D) reconstruction of buildings through multiple coherent SAR images. In order to obtain sufficient signal-to-noise ratio (SNR), typical TomoSAR applications often require dozens of scenes of SAR images. However, limited by time and cost, the available SAR images are often only 3–5 scenes in practice, which makes the traditional TomoSAR technique unable to produce satisfactory SNR and elevation resolution. To tackle this problem, the conditional generative adversarial network (CGAN) is proposed to improve the TomoSAR 3D reconstruction by learning the prior information of building. Moreover, the number of tracks required can be reduced to three. Firstly, a TomoSAR 3D super-resolution dataset is constructed using high-quality data from the airborne array and low-quality data obtained from a small amount of tracks sampled from all observations. Then, the CGAN model is trained to estimate the corresponding high-quality result from the low-quality input. Airborne data experiments prove that the reconstruction results are improved in areas with and without overlap, both qualitatively and quantitatively. Furthermore, the network pretrained on the airborne dataset is directly used to process the spaceborne dataset without any tuning, and generates satisfactory results, proving the effectiveness and robustness of our method. The comparative experiment with nonlocal algorithm also shows that the proposed method has better height estimation and higher time efficiency.

Physical simulations based on partial differential equations typically generate spatial fields results, which are utilized to calculate specific properties of a system for engineering design and optimization. Due to the intensive computational burden of the simulations, a surrogate model mapping the low-dimensional inputs to the spatial fields are commonly built based on a relatively small dataset. To resolve the challenge of predicting the whole spatial field, the popular linear model of coregionalization (LMC) can disentangle complicated correlations within the high-dimensional spatial field outputs and deliver accurate predictions. However, LMC fails if the spatial field cannot be well approximated by a linear combination of base functions with latent processes. In this paper, we present the Extended Linear Model of Coregionalization (E-LMC) by introducing an invertible neural network to linearize the highly complex and nonlinear spatial fields so that the LMC can easily generalize to nonlinear problems while preserving the traceability and scalability. Several real-world applications demonstrate that E-LMC can exploit spatial correlations effectively, showing a maximum improvement of about 40% over the original LMC and outperforming the other state-of-the-art spatial field models.