###### Abstract  
Quantitative studies on surface elements require satellite hyperspectral images with high spatial resolution. The identification of different surface elements requires different characteristic bands and their corresponding optimal spatial-spectral fusion methods. To address these problems, the harmonic analysis (HA), guided filtering, and Gram-Schmidt (GS) algorithms were integrated to propose a spatial-spectral fusion method called HGF. The fusion experiment and validation of the hyperspectral images of GaoFen-5 (GF-5) and ZY1-02D were conducted separately using the HGF method, and the fusion effect was evaluated in three band intervals according to the spectral response of the ground class. First, HGF was used to fuse the GF-5 and GaoFen-1 (GF-1) images, and the fusion effect was evaluated both qualitatively and quantitatively. Second, the optimal fusion method was selected for the corresponding characteristic bands of the different surface elements. Finally, the hyperspectral image obtained by ZY1-02D and multispectral image of Sentinel-2B were used for validation to improve the accuracy and efficiency of satellite hyperspectral images in quantitative studies. The results show that for further studies on soil, vegetation, and water bodies, the best fusion methods in the 390-730, 730-1400, and 1400-2260 nm intervals are the CS, HGF, and HGF algorithms, respectively. Further analysis showed that the HGF or GS methods can be selected for quantitative studies on vegetation and water bodies and that the HGF method exhibits outstanding advantages for quantitative analysis of each soil element. harmonic analysis; spatial-spectral fusion; hyperspectral image; GF-5; ZY1-02D 2  
exhibits better spectral fidelity [2]. Subsequently, scholars performed the fusion of panchromatic and hyperspectral images based on a model with mixed pixel decomposition [3]. With the rapid increase in the spatial resolution of satellite-based images, the ratio in the spatial resolution of images has gradually increased. To effectively integrate the spatial and spectral information of images with large spatial resolution differences, a strategy of stepwise fusion has been proposed with the help of images that exhibit similar spatial resolutions [4]. In recent years, deep learning methods have shown excellent application prospects and are widely used in the fusion of hyperspectral images [5; 6; 7]. Although these methods require a large number of training samples, they can be trained in an unsupervised manner [8; 9]. In 2013, [PERSON] et al. first used the harmonic analysis method to detect small target information in hyperspectral images [10]. From the perspective of the spectral curve of a single image element, better results have been achieved through the fusion of panchromatic and hyperspectral image data from the same satellite as compared to the traditional component replacement method combined with harmonic analysis techniques [11; 12]. Based on the research of [PERSON] et al. (2014) [11], [PERSON] et al. (2015) [12] found that the combination of harmonic analysis and GS transform methods can reduce the pixel gray difference between the harmonic residual terms obtained from the decomposition of high-spatial-resolution images and hyperspectral images. Further analysis reveals that the above algorithms and models are mainly used for feature interpretation [1; 13; 14; 15] and that their application to the quantification of surface elements needs to be explored further. A quantitative study of surface elements requires hyperspectral satellite images with high spatial resolution and spectral fidelity. The optimal image fusion methods and their applicable wavelength intervals differ in the various studies conducted on surface elements. Therefore, the construction of an efficient hyperspectral satellite image fusion model that can be used on satellite data is crucial, considering the need for quantitative studies on different surface elements.