## 3 Experimental Results and Discussion
### Experimental Setup  
The experimental datasets include three well-known individual HS images and a group of spatially co-registered real HS and MS images. For detailed information on these images, we recommend readers to refer to the following literature: [13; 15; 39]. The selected subsets of the first three HS images with 320 \(\times\) 320, 400 \(\times\) 400, and 400 \(\times\) 240 pixels, respectively. To simulate the LR HS images, the HS images were spatially blurred by Gaussian low-pass filters with 3 \(\times\) 3, 7 \(\times\) 7, and 11 \(\times\) 11 sizes, followed by downsampling operations with stride 2 \(\times\) 2, 4 \(\times\) 4, and 6 \(\times\) 6, respectively, whereas the HR MS images were simulated by averaging the original HS bands with the wavelength covered by the corresponding MS bands of Landsat 5 TM sensor. In addition, Gaussian noise with peak-signal-to-noise of 40 dB was added to the MS image to simulate the different imaging conditions of HS and MS images. The last HS image includes 200 \(\times\) 200 pixels and 159 bands after removing the noisy bands. The corresponding MS image acquired by the ASTER imager consisted of three bands and was blurred by applying a Gaussian filter with a \(3\times 3\) size and down-sampled to the original resolution of the HS image. The LR HS image is then simulated by similar operations with the first three datasets. In our experiments, several state-of-the-art hyper-sharpening methods, including CNMF [13], JNMF [15], DPLM [14], and the CNN-based algorithm TCNNF [29], were used to compare with our CpCNNN method. We also adapted the detail-injection-based CNN pan-sharpening method [38] for our hyper-sharpening task (abbreviated to DiCNN) to further validate the superiority of our method. According to the related references [13; 15], 40 end-members were extracted by vertex component analysis for CNMF and JNMF. The dictionary dimensionality of DPLM is also 40, and the optimal sparseness degrees were set to 0.7 for the second dataset and 0.6 for others. For TCNNF and DiCNN, the parameters were set mostly in accordance with the authors' suggestion, including the number of convolutional layers and filters, learning rate, momentum, etc. For fairness, in our CpCNNN method, apart from the filter and patch sizes, parameters were determined basically according to the TCNNF and DiCNNN methods, e.g., the learning rate was fixed as 0.0001, the momentum was set to 0.9, the batch size was 128, and the number of training epochs was 200. The filter number and size of each convolutional layer were set to 32 and 3 \(\times\) 3, respectively, which are illustrated in Section 2. In particular, the last convolutional layer including \(\Lambda\) filters had a 1 \(\times\) 1 size, corresponding to the details of \(\Lambda\) bands for a single pixel. All the weights of convolutional filters were initialized by Gaussian random distributions with a zero-mean and standard deviation of 0.01. To achieve the best performance, the MS image patches of TCNNF and the HS/MS image patches of DiCNNN were composed of 21 \(\times\) 21 pixels, which was determined empirically according to our experiments. For our CpCNNN method, the patch sizes of HS and MS images were set to 5 \(\times\) 5 and 9 \(\times\) 9, respectively, in the following sub-section. Specifically, for these CNN-based methods, including our CpCNNN method, the samples (namely image patches) were generated by selecting each pixel with its neighbors of the HS and MS images, respectively. As mentioned above, the degraded HS image is first interpolated to the size of the MS image. Therefore, for a given degraded HS or MS image with \(n\) pixels, a total of \(n\) training samples, namely \(n\) pixels, are used to train the network. The testing set, thus, has \(N\) samples, corresponding to \(N\) pixels of the HR HS and MS images. The experiments were conducted on Windows 10 operating system based on Anaconda toolkit with Python 3.7. An NVIDIA GeForce RTX 2060 GPU card was used to train the CNN networks.