Global or quasi-global digital elevation model (DEM) datasets provide three-dimensional information on terrain surface, and they have been extremely useful in geoscience research and applications. However, the wide application of DEMs is constrained by differences in the means of observation and processing, and in the resolution of global public DEM datasets. An adaptive regularization variation model based on sparse representation is proposed to generate a high-quality DEM by fusing multi-source DEMs. First, since the sparse representation method has a powerful capability to reconstruct information based on a small amount of information, prior terrain information is extracted from the 90-m TanDEM-X DEM (TDM90) with unprecedented global accuracy using a so-called sparse representation. In this step, an intermediate DEM (termed STDM30) is first extracted from TDM90 that preserves maximum terrain details, thereby preventing the degradation of the DEM accuracy induced by resampling. Then, the designed regularization framework based on terrain slope can constrain the DEM spatial information during fusing multiple datasets. STDM30 is combined with the ALOS Global Digital Surface Model “ALOS World 3D 30 m” (AW3D30) and the 1 arc-second Shuttle Radar Topography Mission Digital Elevation Model (SRTM1) through the designed adaptive regularization variation model to generate a high-accuracy DEM product with a resolution of 30 m. The results of the proposed method were verified by a model-to-model comparison in South Dakota as well as by validation against GPS benchmarks in Southern California. The RMSE, MAE, and SD of the fused DEM are all lower than those of the existing public DEMs, especially in terms of removing topographic noise and refining terrain details. The GPS validation showed that the fused DEM has an RMSE of 3.04 m, with the highest absolute accuracy among the four studied DEMs, and its errors are almost equal to the normal distribution. These experimental results confirm that the multi-scale and multi-source DEM fusion strategy combining sparse representation and an adaptive regularization variation model can utilize existing public datasets and effectively improve the quality of global DEM products.

全球或准全球数字高程模型（DEM）数据集可在地形表面上提供三维信息，并且在地球科学研究和应用中非常有用。但是，DEM的广泛应用受到观察和处理方式以及全球公共DEM数据集解析的差异的限制。提出了一种基于稀疏表示的自适应正则化变化模型，通过融合多源DEM生成高质量的DEM。首先，由于稀疏表示方法具有基于少量信息来重建信息的强大功能，因此使用所谓的稀疏表示以前所未有的全局精度从90米TanDEM-X DEM（TDM90）中提取了先验地形信息。在这一步中 首先从TDM90中提取一个中间DEM（称为STDM30），该DEM保留了最大的地形细节，从而防止了因重采样而导致的DEM精度下降。然后，基于地形坡度设计的正则化框架可以在融合多个数据集的过程中约束DEM空间信息。STDM30与ALOS全球数字地面模型“ ALOS World 3D 30 m”（AW3D30）和1弧秒航天飞机雷达地形任务数字高程模型（SRTM1）结合在一起，通过设计的自适应正则化变化模型来生成高精度DEM分辨率为30 m的产品。通过在南达科他州进行模型间比较以及通过对南加州的GPS基准进行验证，验证了该方法的结果。RMSE，MAE，融合的DEM的SD和SD都低于现有的公共DEM，尤其是在消除地形噪声和优化地形细节方面。GPS验证表明，融合的DEM的RMSE为3.04 m，在四个研究的DEM中绝对精度最高，其误差几乎等于正态分布。这些实验结果证实，将稀疏表示和自适应正则化变化模型相结合的多尺度和多源DEM融合策略可以利用现有的公共数据集，并有效地提高全球DEM产品的质量。在四个研究的DEM中绝对精度最高，其误差几乎等于正态分布。这些实验结果证实，将稀疏表示和自适应正则化变化模型相结合的多尺度和多源DEM融合策略可以利用现有的公共数据集，并有效地提高全球DEM产品的质量。在四个研究的DEM中绝对精度最高，其误差几乎等于正态分布。这些实验结果证实，将稀疏表示和自适应正则化变化模型相结合的多尺度和多源DEM融合策略可以利用现有的公共数据集，并有效地提高全球DEM产品的质量。