# Learning an Efficient Convolution Neural Network for Pansharpening
## 4 Experiment
### Experimental Results and Analysis
#### 4.2.2 Original Scale Experiment  
Since our CNN model is implemented at a reduced scale, we also fused the original LRMS and PAN for the sake of assessing the ability of transferring to original scale. Specifically, the raw MS image was up-sampled (LRMS) at the scale of PAN image, and we inputted the LRMS and corresponding PAN image into our model to yield full-resolution results. Same as the previous subsection, a typical example of WorldView-2 is displayed in Figure 8, and we also display the residual images in Figure 9. As the LRMS can be regarded as the low-pass component of HRMS, the optional residual in this section should be the high-frequency content of the desired HRMS, which means sharp edges without smooth regions.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Q**8 & **Q** & **SAM** & **ERGAS** & **SCC** & **Time** \\ \hline
**Reference** & 1 & 1 & 0 & 0 & 1 & 0 \\
**BDSD** & 0.8224 & 0.8080 & 5.9732 & 4.0023 & 0.8145 & 0.25 s (CPU) \\
**NIHS** & 0.7770 & 0.7642 & 5.1216 & 4.2357 & 0.7668 & 2.55 s (CPU) \\
**Indusion** & 0.7948 & 0.7982 & 5.0844 & 3.8993 & 0.8016 & 0.17 s (CPU) \\
**NMRA** & 0.8487 & 0.8413 & 4.5072 & 3.2280 & 0.8741 & 0.19 s (CPU) \\
**\(\ell\)1/2** & 0.8065 & 0.7880 & 4.7067 & 4.0404 & 0.7106 & 12.56 s (CPU) \\
**PNN** & 0.8377 & 0.8459 & 5.0428 & 3.1775 & 0.9005 & 0.61 s (GPU) \\
**MSDCNN** & 0.8741 & 0.8580 & 4.3776 & 2.7740 & 0.9149 & 0.14 s (GPU) \\
**Proposed** & 0.8772 & 0.8758 & 3.7132 & 2.4658 & 0.9258 & 0.07 s (GPU) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Performance indicators of a WorldView-2 image at reduced scale.  
Figure 7: The residual images corresponding to Figure 6. **(a)** BDSD; **(b)** NIHS; **(c)** Indusion; **(d)** NMRA; **(e)**\(\ell 1/2\); **(f)** PNN; **(g)** MSDCNN; **(h)** Proposed.  
Given the absence of HRMS at original scale, three reference-free numeric metrics were adopted to quantify the qualities of fusion results, i.e., quality with no-reference index (QNR) [41], spectral component of QNR \((D_{\lambda})\) and spatial component of QNR \((D_{S})\). Apart from the three aforementioned non-reference metrics, we also followed Reference [42] by down-sampling the pansharpened results and compare the down-sampled results with the raw MS images. We tested the SAM and SCC indicators for spectral and spatial quality measurements, and the assessment results are summarized in Table 2.  
Figure 8: Results of the original scale experiment on an area extracted from a WorldView-2 image. (**a**) LRMS; (**b**) PAN; (**c**) BDSD; (**d**) NIHS; (**e**) Indusion; (**f**) NMRA; (**g**) \(\ell 1/2\); (**h**) PNN; (**i**) MSDCNN; (**j**) Proposed.  
Figure 9: The residual images corresponding to Figure 8. (**a**) BDSD; (**b**) NIHS; (**c**) Indusion; (**d**) NMRA; (**e**) \(\ell 1/2\); (**f**) PNN; (**g**) MSDCNN; (**h**) Proposed.  
By comparing the images displayed in Figures 8 and 9, we can observe similar tendency as that of previous reduced scale experiments: NIHS and \(\ell\)1/2 preserve precise spectral information, while the spatial domains were rarely sharpened. Among the remaining results, BDSD introduces severe block artifacts, and Indusion and NMRA return images with competitive performance; however, when they come to residual analysis, we can find obvious spectral distortions. PNN and MSDCNN remain competitive in spatial details enhancement, while the proposed network performed better in preserving spectral details, which can be observed from the corresponding residual images.