Height estimation from a single Synthetic Aperture Radar (SAR) image has demonstrated a great potential in real-time environmental monitoring and scene understanding. The projection of a single 2D SAR image from multiple 3D height maps is an ill-posed problem in mathematics. Although Unet has been widely used for height estimation from a single image, the ill-posed problem cannot be completely resolved, and it leads to deteriorated performance with limited training data. This paper tackles the problem by Unet with the help of supplementary sparse height information and proxyless neural architecture search (PDPNAS) for Unet. The sparse height, which can be accepted from low-resolution SRTM or LiDAR products, is included as the supplementary information and is helpful to improve the accuracy of the estimated height map, especially in mountain areas with a wide range of elevations. In order to explore the effect of sparsity of sparse height on the estimated height map, a parameterized method is proposed to generate sparse height with a different sparse ratio. In order to further improve the accuracy of the estimated height map from a single SAR imagery, PDPNAS for Unet is proposed. The optimal architecture for Unet can be searched by PDPNAS automatically with the help of a depth-aware penalty term p. The effectiveness of our approach is evaluated by visual and quantitative analysis on three datasets from mountain areas. The root mean squared error (RMSE) is reduced by 90.30% through observing only 0.0109% of height values from a low-resolution SRTM product. Furthermore, the RMSE is reduced by 3.79% via PDPNAS for Unet. The research proposes a reliable method for estimating height and an alternative method for wide-area DEM mapping from a single SAR image, especially for the implementation of real-time DEM estimation in mountain areas. © 2022 by the authors.
