## 5 Conclusions  
In this paper, a novel MS and PAN images fusion method based on WMCF decomposition is proposed. A WLSF-based method is used to fuse all the bands of the MS image to generate the intensity component \(IC\). In accordance with an image matting model, \(IC\) is used as the original \(\alpha\) channel for spectral estimation to obtain a foreground image \(F\) and a background image \(B\). WMCF and GF are used to decompose a PAN image into three scales, i.e., a small scale (\(SS\)) image, a large scale (\(LS\)), and a basic image, respectively. Then, a MSMDM-guided PAC-PCNN fusion strategy is used to fuse \(IC\) and the basic image obtained from the PAN image. All parameters in the PAC-PCNN model can be automatically calculated in accordance with the inputs with a fast convergence speed. Finally, the fused images, and the \(LS\) and \(SS\) image are combined as the last \(\alpha\) channel. In accordance with an image matting model, the foreground color \(F\), background color \(B\) and the last \(\alpha\) channel are reconstructed to obtain the final fused image. The experimental results show that the method proposed in this paper has better performance than some representative pan-sharpening methods and can solve the problem of spatial distortion and spectral distortion.  
We conducted experiments using four different image pairs to compare with ten representative pan-sharpening methods. The experimental results show that the proposed method can achieve superior results in terms of visual effects and objective evaluation. The proposed method can obtain more spatial details from the PAN image with higher efficiency while retaining more spectral information contained in the MS image. By fusing the MS and PAN images, the fused images have both higher spatial detail representation ability and retain the spectral features contained in the MS images, which can obtain a richer description about the target information. With the improvement of remote sensing satellite sensor technology, the information integration and processing technology has been enhanced. Thus, the proposed method can be better applied to various aspects, such as military reconnaissance, remote sensing measurements, forest protection, vegetation cover, image classification and machine vision.  
In the future research, we will work on developing more effective fusion strategies and explore the application of our method in other fields.  
**Author Contributions:** Conceptualization, Y.P.; methodology, Y.P.; software, S.X.; validation, S.X.; formal analysis, Y.P.; investigation, S.X.; resources, Y.P.; data curation, S.X.; writing--original draft preparation, Y.P.; writing--review and editing, Y.P., D.L. and J.A.B.; visualization, Y.P.; supervision, D.L. and J.A.B.; project administration, D.L.; funding acquisition, L.W. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This paper was supported by Leading Talents Project of the State Ethnic Affairs Commission and National Natural Science Foundation of China (No. 62071084).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.