# Hyperspectral Image Super-Resolution Based on Spatial Group Sparsity Regularization Unmixing
## 6 Conclusions  
This paper proposed an HSI super-resolution method based on spatial group sparsity regularization unmixing. It can construct a high spatial and spectral resolution HSI from a low spatial resolution HSI and a high spatial resolution conventional image by solving the spectral unmixing problem for both input images. The unmixing-based super-resolution of the HSI helps to alleviate the  
Figure 12: Classification results of our method on the UNIVERSITY OF PAVIA data set.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Methods** & **Reference** & **FUSE** & **BSR** & **CSU** & **CMS** & **LTTR** & **Ours** \\ \hline OA & 72.06\% & 70.39\% & 70.07\% & 71.43\% & 69.84\% & 70.82\% & 71.84\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: Classification result comparison for the UNIVERSITY OF PAVIA data set.  
constraints derived from the imaging process. Under the linear mixing model, the proposed unmixing method integrates the advantages of both spatial group sparsity and the \(\ell_{2,1}\) norm to produce a more accurate and robust unmixing estimation. The SLIC superpixel algorithm is used to transform the original hyperspectral data, making full use of the spatial information and sparse priors. The SLIC superpixel algorithm is used to transform the original HSI into spatial groups. Then, the distribution of the endmembers is estimated based on the spatial and sparsity priors. The proposed method takes advantage of this distribution estimate as a regularizer for sparse unmixing and solves for the abundances using the ADMM algorithm. The spatial group sparsity regularization unmixing makes full use of the spatial structure and the spectra of the images. In simulations on public data sets--a ground-based data set \"Harvard\" and five satellite remote sensing data sets--the proposed method showed superior performance, when compared to state-of-the-art methods.  
All authors conceived this work together. [PERSON]. ([PERSON]) developed the mathematical formulation, implemented the software, prepared the data, and executed the experiments. [PERSON]. ([PERSON]) also led the writing of the manuscript. [PERSON] and [PERSON] administrated the project and supervised the research. All authors have read and agreed to the published version of the manuscript.  
This work was partially supported by the National Key Research and Development Program of China (No. 2017 YFB1301104 and 2017 YFB1001900), and the National Natural Science Foundation of China (No. 91648204 and 61803375). The authors acknowledge the State Key Laboratory of High Performance Computing, National University of Defense Technology, P.R. China. The support provided by the China Scholarship Council (CSC) and [PERSON] and [PERSON] Chair for Engineering Design of University of Toronto is gratefully acknowledged.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
HSI Hyperspectral image MSI Multispectral image HS-MS image fusion Hyperspectral and multispectral image fusion SLIC Simple linear iterative clustering ADMM Alternative direction method of multipliers MRA Multi-resolution analysis NMF Non-negative matrix factorization SRF Spectral response functions PSF Point spread functions LTTR Low tensor-train rank CNN convolutional neural network KNN K-nearest neighbors