The digital elevation model (DEM) is known as one kind of the most significant fundamental geographical data models. The theory, method and application of DEM are hot research issues in geography, especially in geomorphology, hydrology, soil and other related fields. In this paper, we improve the efficient sub-pixel convolutional neural networks (ESPCN) and propose recursive sub-pixel convolutional neural networks (RSPCN) to generate higher-resolution DEMs (HRDEMs) from low-resolution DEMs (LRDEMs). Firstly, the structure of RSPCN is described in detail based on recursion theory. This paper explores the effects of different training datasets, with the self-adaptive learning rate Adam algorithm optimizing the model. Furthermore, the adding-“zero” boundary method is introduced into the RSPCN algorithm as a data preprocessing method, which improves the RSPCN method’s accuracy and convergence. Extensive experiments are conducted to train the method till optimality. Finally, comparisons are made with other traditional interpolation methods, such as bicubic, nearest-neighbor and bilinear methods. The results show that our method has obvious improvements in both accuracy and robustness and further illustrate the feasibility of deep learning methods in the DEM data processing area.

中文翻译：

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RSPCN：基于递归子像素卷积神经网络的数字高程模型超分辨率

数字高程模型（DEM）被称为一种最重要的基础地理数据模型。DEM的理论、方法和应用是地理学研究的热点问题，尤其是地貌学、水文、土壤等相关领域。在本文中，我们改进了高效的亚像素卷积神经网络 (ESPCN) 并提出了递归亚像素卷积神经网络 (RSPCN)，以从低分辨率 DEM (LRDEM) 生成更高分辨率的 DEM (HRDEM)。首先，基于递归理论详细描述了RSPCN的结构。本文探讨了不同训练数据集的效果，自适应学习率Adam算法对模型进行了优化。此外，在RSPCN算法中引入了加“零”边界法作为数据预处理方法，这提高了 RSPCN 方法的准确性和收敛性。进行了大量实验以训练该方法直至达到最优。最后，与其他传统插值方法进行了比较，例如双三次、最近邻和双线性方法。结果表明，我们的方法在准确性和鲁棒性上都有明显的提升，进一步说明了深度学习方法在DEM数据处理领域的可行性。