###### Abstract
This is achieved through an encoder-decoder architecture, which establishes a mapping relationship between features and 3D volumes [14]. However, although deep-learning-based reconstruction methods overcome the challenges faced by traditional methods and show advantages in dealing with appearance variations, their generalization capabilities are still limited when facing unseen viewpoints and scenes. Furthermore, these methods require large amounts of data and computing resources to train the models and rely on real 3D models for supervised learning. Recently, methods based on neural radiance fields [15] have demonstrated great potential in the area of novel view synthesis and 3D reconstruction due to their compact model and realistic rendering effects. Refs. [11; 16] studied multi-view satellite images' 3D reconstruction based on neural radiance fields. They used satellite images captured from different viewpoints to implicitly model the scene and synthesize novel views and 3D models of the scene. As shown in Figure 1, a set of multi-view satellite images and their corresponding pose information are taken as inputs to generate a novel view, depth map, or mesh model of the scene. Compared with traditional stereo-vision-based methods and deep learning methods, the 3D reconstruction of satellite images based on neural radiance fields has the advantages of end-to-end and self-supervision. At the same time, the NeRF learns a continuous volume representation of the scene, enabling it to uniquely integrate different properties of physical scenes, such as surface radiance and illumination. This allows it to handle complex situations in a natural manner, including changes in appearance. [PERSON] et al. [11] first explored the use of the NeRF for 3D reconstructions of satellite images and proposed shadow neural radiance field (S-NeRF), which are specially designed to reconstruct the appearance and geometry of the terrestrial surface from satellite images. Sat-NeRF [16] further combines some recent trends in neural rendering with the rational polynomial coefficient (RPC) model and deals with transient phenomena, such as cars and vegetation, that cannot be explained by the sun's position through a shadow-aware irradiance model and uncertainty weights. These studies demonstrate the great potential of using the NeRF for satellite photogrammetry missions. However, these methods, like most NeRF model methods, usually require 8-10 h or even longer for training and optimization, which limits their application in practical scenarios. In this work, we propose a new efficient remote sensing neural radiance field variant, called SatelliteRF, to efficiently model the Earth's terrain based on satellite imagery. SatelliteRF uses multi-resolution hash position encoding [17] to reduce the size of the multi-layer perceptron (MLP), which speeds up model training and improves the efficiency of scene reconstruction. To address issues such as illumination variations in satellite images, SatelliteRF represents the scene as a static surface with an albedo color and a radiance model, with the rendered color determined by the product of the albedo and radiance models. In addition, SatelliteRF effectively models transient elements, such as cars and shadows, in the scene by learning the transient embeddings for each image. In order to further improve the quality of scene reconstruction, we adopt a random structural similarity loss function and utilize the rich structural information in remote sensing images to train the model. Our experiments on the DFC 2019 dataset [18,19] shows that SatelliteRF not only achieves a superior reconstruction quality but also reduces the training time for the same region from 8\(\sim\)10 h to 5\(\sim\)10 min. Our key contributions are summarized as follows:  
* We significantly improve the speed of the 3D reconstruction of multi-view satellite images by using multi-resolution hash encoding and smaller MLP networks.