# Hyperspectral Image Super-Resolution Based on Spatial Group Sparsity Regularization Unmixing
## 4 Experiments
### Data Sets and Quantitative Metrics  
We used real-world images from standard HSI data sets, namely, the \"Harvard\" data set [36] and remote sensing image data sets. The remote sensing data we used were \"CUPRITE\", \"CHIKUSEI\", \"INDIAN PINES\", \"UNIVERSITY OF PAVIA\", and \"UNIVERSITY OF HOUSTON\". Images in the \"Harvard\" data set have a spatial resolution of \(1392\times 1040\) and contain 31 spectral bands ranging from 420 nm to 720 nm. RGB color images from the \"Harvard\" data set are shown in Figure 1. In our experiments, the original images in the data sets served as ground truth. The observed low spatial resolution HSIs were downsampled by a factor of 8. Similarly, the conventional images (RGB color images) were downsampled in the spectral domain with a spectral response matrix \(R\) derived from a Nikon D700 digital camera (Nikon D700 Study [[http://www.maxmax.com/nikon_d700_study.htm](http://www.maxmax.com/nikon_d700_study.htm)]([http://www.maxmax.com/nikon_d700_study.htm](http://www.maxmax.com/nikon_d700_study.htm))). CURPRITE is a data set which was captured in 1995 by the AVIRIS sensor over the Cuprite mining district in Nevada, shown in Figure 2a; CHIKUSEI was acquired in 2014 by a Headwall Hyperspectral Visible and Near-Infrared imaging sensor, shown in Figure 2b; INDIAN PINES is a data set captured in 1992 by the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) sensor over the Indian Pines test site in northwestern Indiana, shown in Figure 2c; UNIVERSITY OF PAVIA was taken by The Reflective Optics Spectrographic Imaging System (ROSIS)-3 optical airborne sensor over the University of Pavia in 2003, as shown in Figure 2d; and the UNIVERSITY OF HOUSTON data set was acquired by an ITRES Compact Airborne Spectrographic Imager (CASI)-1500 sensor over the University of Houston campus in 2013, as shown in Figure 2e. The main specifications of all the remote sensing data sets are summarized in Table 1. It must be noted that we used cropped images with selected spectral bands, instead of the original images. Lines 4 and 6 in Table 1 show the number of selected bands and the size of the cropped image, which are essential parameters for the algorithms. Figure 1: Images from the Harvard data set. Six widely accepted quantitative metrics were used in this work to quantitatively measure the results. The basic idea of Structural Similarity (SSIM) [1] is to evaluate the similarity of two images through the following three aspects: luminance, contrast, and structure. It is formulated as follows:  
\[ \begin{split} SSIM&=f(l(S,\hat{S}),c(S,\hat{S}),s(S, \hat{S}))\\ l(S,\hat{S})&=\frac{2\mu_{S}\mu_{\hat{S}}+C_{1}}{ \mu_{S}^{2}+\mu_{S}^{2}+C_{1}},\ \ c(S,\hat{S})=\frac{2\sigma_{S}\sigma_{\hat{S}}+C_{2}}{ \sigma_{S}^{2}+\sigma_{S}^{2}+C_{2}},\ \ s(S,\hat{S})=\frac{\sigma_{S\hat{S}}+C_{3}}{ \sigma_{S}\sigma_{S}+C_{3}},\end{split}  \tag{20}\]  
where \(\mu_{S}\) and \(\mu_{\hat{S}}\) represent the average values of the estimated image and ground truth, \(\sigma\) is the standard deviation, and \(\sigma_{S\hat{S}}\) is the covariance of \(S\) and \(\hat{S}\). A SSIM value close to one indicates high image quality. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Data Sets** & **CUPRITE** & **CHIKUSEI** & **INDIAN PINES** & **PAVIA** & **HOUSTON** \\ \hline Spectral range (\(\mu\)m) & 0.4–2.5 & 0.36–1.02 & 0.4–2.5 & 0.43–0.84 & 0.36–1.05 \\ Total bands & 224 & 128 & 224 & 115 & 144 \\ Used bands & 185 & 128 & 192 & 103 & 144 \\ Total image size & 512 \(\times\) 614 & 2517 \(\times\) 2335 & 512 \(\times\) 614 & 610 \(\times\) 340 & 349 \(\times\) 1905 \\ Used image size & 420 \(\times\) 360 & 540 \(\times\) 320 & 360 \(\times\) 360 & 560 \(\times\) 320 & 320 \(\times\) 540 \\ Ground Sampling Distance & 20 & 2.5 & 20 & 1.3 & 2.5 \\ SNR & 35 & 35 & 35 & 35 & 35 \\ \hline \end{tabular}
\end{table} 
Table 1: Main specifications of the remote sensing data sets. Figure 2: Remote sensing images  
The root mean square error (RMSE) [1] measures the absolute error between the estimated image and the ground truth.