# Panchromatic and Multispectral Image Fusion Combining GHS, NSST, and PCA
###### Abstract  
Spatial and spectral information are essential sources of information in remote sensing applications, and the fusion of panchromatic and multispectral images effectively combines the advantages of both. Due to the existence of two main classes of fusion methods--component substitution (CS) and multi-resolution analysis (MRA), which have different advantages--mixed approaches are possible. This paper proposes a fusion algorithm that combines the advantages of generalized intensity-hue-saturation (GIHS) and non-subsampled shearlet transform (NSST) with principal component analysis (PCA) technology to extract more spatial information. Therefore, compared with the traditional algorithms, the algorithm in this paper uses PCA transformation to obtain spatial structure components from PAN and MS, which can effectively inject spatial information while maintaining spectral information with high fidelity. First, PCA is applied to each band of low-resolution multispectral (MS) images and panchromatic (PAN) images to obtain the first principal component and to calculate the intensity of MS. Then, the PAN image is fused with the first principal component using NSST, and the fused image is used to replace the original intensity component. Finally, a fused image is obtained using the GIHS algorithm. Using the urban, plants and water, farmland, and desert images from GeoEye-1, WorldView-4, GaoFen-7 (GF-7), and Gaofen Multi-Mode (GFDM) as experimental data, this fusion method was tested using the evaluation mode with references and the evaluation mode without references and was compared with five other classic fusion algorithms. The results showed that the algorithms in this paper had better fusion performances in both spectral preservation and spatial information incorporation. image fusion; generalized intensity-hue-saturation (GIHS) algorithm; non-subsampled shearlet transform (NSST); principal component analysis (PCA); bootstrap filter  
1  
<ccs2012> <  
incorporate high-frequency spatial information, and, finally, a fused image is obtained through inverse transformation. Typical component substitution (CS) methods include principal component analysis (PCA) and the Gram-Schmidt process (GS). In addition, in recent years, methods based on deep learning [3,4] have also achieved good results, but their computational complexity is high, and they are not suitable for large-scale remote sensing images; thus, this paper does not discuss them in depth. The spatial methods include multi-resolution analysis (MRA), which decomposes MS and PAN at multiple scales. The high-frequency components are fused with low-frequency components using different rules and, finally, inverted back to the fused image. Typical MRA methods include wavelet transform [5], curvelet transform [6], contourlet transform [7,8], non-subsampled contourlet transform (NST) [9], non-subsampled shearlet transform (NSST) [10], and so on. Among these, wavelet transform is the most widely used MRA method, but its direction selectivity is limited and it cannot achieve a stable fusion effect. The curvelet and contourlet transforms have no translation invariance, and the fusion result may be affected by the noise or alignment accuracy of the source image. NCST has high computational complexity, so it is unsuitable for large images. NSST has good directional selectivity, can obtain more information from the source image, and has no down-sampling operation in the decomposition process, thus effectively reducing the pseudo-Gibbs phenomena caused by the registration accuracy. The CS approaches have good spatial quality but severe spectral distortion, while the MRA class methods have high spectral fidelity but poor spatial quality. These two types of method are complementary [11], which has given rise to many coupled methods.