# Pansharpening by Complementing Compressed Sensing with Spectral Correction
## 3 Results
### Experimental Results  
Table 4 shows the effect of the back-projection (BP). The results of the intensity \(I_{sr}\) obtained using the sparse representation (SR) and the intensity obtained by repeating BP ten times with a size 5 filter are shown. These were compared by CC, UIQI, and ERGAS, and applying BP was better in all cases. Table 5 shows the effect of the tradeoff process (TP). The intensity images generated by SCMP, SR, and TP are shown. TP was the best in all evaluations. Table 6 shows the comparison of BP and TP TP was better in every case. Tables 7 and 8 show numerical evaluations of the existing methods and the proposed method. The existing methods include fast IHS [5], Gram-Schmidt method (GS) [7], band-dependent spatial detail (BDSD) [41], weighted least-squares (WLS)-filter-based method (WLS) [42], multiband images with adaptive spectral-intensity modulation (MDSIm) [43], spectrum correction using modeled panchromatic image (SCMP) [35], image super-resolution via sparse representation (ISSR) [13] using natural images (Dict-natural) and corresponding images (Dict-self), the sparse representation of injected details (SR-D) [30], and the method of sparse representation described by [PERSON] et al. (SRayas) [34]. The size of the local estimation of the distinct block of BDSD was \(256\times 256\) for Nihonmatsu and \(448\times 448\) for Yokohama. For the ISSR settings, the training images for the dictionary included training PAN images and natural images, the number of training times was 40, the number of atoms in the dictionary was 1024, the atom size of the dictionary was \(4\times 4\times 5\), the sparsity regularization parameter was 0.1, randomly selected 1000 training image patches were used, the upscale was 4 (ratio of resolution of PAN images and MS images of IKONOS), overlap pixel of patches in the reconstruction process was \(\mathbb{R}^{1\times p}\) in horizontal direction and \(\mathbb{R}^{p\times 1}\) in vertical direction, the size of the back-projection filter was \(5\times 5\), and the number of iterations was 10. For SR-D, high-resolution and low-resolution dictionaries were constructed from the original PAN images without training. The atom size of the high-resolution dictionary was \(\mathbb{R}^{28\times 28\times 4}\) and the overlapping areas of the adjacent atoms were \(\mathbb{R}^{16\times p},\mathbb{R}^{p\times 16}\); the atom size of the low-resolution dictionary was \(\mathbb{R}^{7\times 7\times 4}\) and and the overlapping area of the adjacent atoms were \(\mathbb{R}^{4\times p},\mathbb{R}^{p\times 4}\).For the SRayas setting, the original IKONOS MS images were used as the training images for the dictionary, the number of training times was 20, the number of atoms in the dictionary \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**CC**} & \multicolumn{2}{c}{**UIQI**} & \multicolumn{2}{c}{**ERGAS**} \\  & **Nihonmatsu** & **Yokohama** & **Nihonmatsu** & **Yokohama** & **Nihonmatsu** & **Yokohama** \\ \hline Ideal & \multicolumn{2}{c}{1.0} & \multicolumn{2}{c}{1.0} & \multicolumn{2}{c}{0.0} \\ \hline ideal & \multicolumn{2}{c}{1.0} & \multicolumn{2}{c}{1.0} & \multicolumn{2}{c}{1.0} \\ \hline fast IHS [5] & 0.783 & 0.914 & 0.717 & 0.901 \\ \hline GS [7] & 0.508 & 0.860 & 0.373 & 0.838 \\ \hline BDSD [41] & 0.860 & 0.887 & 0.864 & 0.851 \\ \hline WLS [42] & 0.866 & 0.884 & 0.870 & 0.759 \\ \hline MDSIm [43] & 0.791 & 0.865 & 0.736 & 0.823 \\ \hline SCMP [35] & 0.883 & 0.928 & 0.864 & 0.910 \\ \hline ISSR (Dict-natural) [13] & 0.831 & 0.765 & **0.918** & 0.704 \\ \hline ISSR (Dict-self) [13] & 0.831 & 0.759 & 0.917 & 0.701 \\ \hline SR-D & 0.845 & 0.786 & 0.914 & 0.710 \\ \hline SRayas [34] & 0.787 & 0.758 & 0.851 & 0.703 \\ \hline Proposed & **0.906** & **0.937** & 0.903 & **0.918** \\ \hline \end{tabular}
\end{table} 
Table 7: Numerical evaluation of the existing methods and the proposed method by CC and UIQI. The highest scores are printed in bold, and the second highest scores are underlined.