## 3 Experimental Results and Discussion
### Parameter Discussion  
Finally, we would like to give a brief analysis of the parameters that may have certain effects on the fusion results in our presented method. Most parameters of our method were determined empirically according to the massive references, e.g., learning rate, batch size, number of epochs, and filter numbers. The 3 \(\times\) 3 filter size is also suggested by numerous related works. Since the numbers of convolutional layers highly depend on the patch sizes in this network, we will focus on discussing two peculiar parameters, namely the patch sizes of HS and MS images. Figures 8 and 9 show the ERGAS and UIQI values of our method with respect to the patch sizes of HS and MS images, respectively. Due to the limitation of page length, only the results under a resolution ratio of 4 (i.e., \(s=4\)) are plotted. However, similar results and conclusions can also be observed under different resolution ratios.  
As a matter of fact, pixels that are far from the center pixel scarcely affect the spectral and spatial details of the current pixel. Thus, a large local area is not necessary for predicting the features of this pixel. On the contrary, a larger patch size usually means that a more complicated architecture of network should be constructed to properly extract the structure information, which generally requires more training samples to obtain a stable network. Therefore, a proper size of patch deserves to be estimated. Meanwhile, it should  
Figure 8: The relative dimensionless global error in synthesis (ERGAS) and universal image quality index (UIQI) values with respect to the patch size of HS image. (**a**) University of Pavia; (**b**) Pavia City center; (**c**) Washington DC Mall; (**d**) San Francisco.  
Figure 7: Local enlargements of fusion result of San Francisco. (**a**) CNMF; (**b**) JNMF; (**c**) DPLM; (**d**) LR HS image; (**e**) TCNNF; (**f**) DiCNN; (**g**) CpCNN; (**h**) Reference HR IS image.  
also be noted that the coupled network aims at exploiting the collaborative spectral and spatial features for HS and MS images, respectively. Nevertheless, the HS sub-network substantially focuses on approximating a spectrum for an unknown pixel according to its nearest neighbors, whereas the MS sub-network focuses on predicting the details by exploring the spatial correlations within a larger local area. As it is well-recognized that HS and MS image have different spatial resolutions, which means they substantially locate on different spatial scales from the viewpoint of multi-scale model, it is natural that using different sizes of patches will benefit the training of network.  
From Figure 8, we can see that, generally, the patch size of \(5\times 5\) or \(7\times 7\) is a relatively proper choice for the HS sub-network. A larger patch size does not help improve the performance. Sizes larger than \(11\times 11\) are not recommended in our method. On the other hand, Figure 9 suggests that for the patch size of MS sub-network, the optimal results occur around \(9\times 9\) and \(11\times 11\). Since the MS image has higher spatial resolution than HS image, the patch size is commonly larger than that of the HS image in order to fully explore the spatial relations of neighboring pixels. Therefore, sizes smaller than \(7\times 7\) or larger than \(13\times 13\) are not recommended in our network. This is basically in accordance with the above theoretical analyses.  
Consequently, in the experiments of Section 3.2., the patch sizes of HS and MS images are set to \(5\times 5\) and \(9\times 9\), respectively, without exception. As mentioned in Section 2.2., the two sub-networks, thus, contain 2 and 4 convolutional layers, respectively, without exception either.