数字高程模型（Digital Elevation Model，简称DEM）是描述地球表面地形特征的数字表示，可以直接理解为由坐标和对应高程值组成的二维向量。高分辨率DEM能够提供更加精准的基础地理数据，被广泛应用于水文、农业等各个不同领域中，获得精确的高分辨率DEM 具有重要的意义和作用。然而，实际应用中，基于现有的测量技术，需要通过硬件设备来获取高分辨率 DEM，而这些设备工作往往需要耗费很大的成本，且获得的高分辨率DEM精度难以保证，获取大面积高分辨率DEM数据更是一项困难的任务。为了提高获取高分辨率DEM的效率和精度，有效利用地形所具有的自相似性，本文提出基于参数化卷积和自相似特性的DEM超分辨率重建模型。

论文的主要工作包括：（1）结合地形的自相似性，利用参数化卷积的思想，针对DEM超分辨率重建实验，应用最适合的参数化基底，实现同时具有平移等变性、旋转等变性和反射等变性的等变卷积。（2）利用等变卷积构建能够实现超分辨率重建任务的等变卷积网络，结合增强深度超分辨率网络（简称EDSR），完成DEM的超分辨率重建模型，提高DEM超分辨率生成数据的精确度。

实验结果表明，相比于传统的卷积（CNN）和其他的等变卷积，如群等变卷积（G-CNN）和基于傅里叶级数展开的滤波器参数化等变卷积（F-Conv），在相同条件下，本文应用的基于偏微分算子的等变卷积（PDO-eConv）能够有效且稳定地提高对应模型DEM超分辨率生成数据的精度。

A Digital Elevation Model (DEM) is a digital representation that describes the topographic features of the earth's surface. It can be directly considered as a two-dimensional vector composed of coordinates and corresponding elevation values. High-resolution DEM can provide basic geographic data more precisely, which is widely used in various fields such as hydrology and agriculture. It is of great significance and role to obtain accurate high-resolution DEM. However, in practical applications, based on the existing measurement technology, it is necessary to obtain high-resolution DEM data by hardware equipment, and the equipment often cost a lot of money. It is also a difficult task to obtain lots of high-resolution DEM data by this way. At the same time, the accuracy of high-resolution DEM is difficult to guarantee, too. In order to improve the efficiency and accuracy of obtaining high-resolution DEM, and effectively use the self-similarity of terrain, this paper proposes a DEM super-resolution reconstruction model based on parameterized convolution and self-similarity.

The main contributions of this dissertation are as follows: (1) Combining the self-similarity of terrain and the idea of filter parameterization, this paper applies the most suitable parameterized bases for DEM super-resolution reconstruction experiment, and constructs the equivariant convolutions with translation equivariance, rotation equivariance and reflection equivariance simultaneously. (2) The proposed equivariant convolution is used to construct an equivariant convolution network for super-resolution reconstruction tasks. Combined with the EDSR(Enhanced Deep Residual Networks for Single Image Super-Resolution), the DEM super-resolution reconstruction model is completed, and the accuracy of DEM super-resolution generated data is improved.

The experimental results show that compared with the traditional convolutional neural network (CNN) and other equivariant convolutions, which includes group equivariant convolution (G-CNN) and filter parameterized equivariant convolution based on Fourier series expansion (F-Conv), the equivariant convolution based on partial differential operator (PDO-eConv) applied in this paper can effectively and stably improve the accuracy of the data generated by the corresponding model DEM super-resolution under the same conditions.