# Gradient-Guided and Multi-Scale Feature Network for Image Super-Resolution
## 3 Proposed Network
### Adaptive Channel Attention Block  
Previous studies [15; 33] have revealed that the super-resolution performance can be further improved by incorporating the channel attention mechanism into the SR model. Specifically, the feature representation ability of the CNN model is maximized by assigning different attention degrees to the different channel features. Inspired by SENet [48], RCAN [15] incorporates the channel attention mechanism into its model and performs the dimensionality reduction operation on feature channels, which effectively improves the visual quality of the reconstructed image and viably diminishes the complexity of the model. Unlike SENet, which performs the fully connected operation on all channels, RCAN only performs fully connected on channels obtained through dimensionality reduction. As pointed out in Ref. [20], the dimensionality reduction operation destroys the direct correlation between the channel and its weight, and the acquired channel attention dependences are wasteful and useless. In order to address the adverse impacts of dimensionality reduction operations on channel attention, we integrate the adaptive channel attention block (ACAB) into the proposed network to explore the correlation dependencies between channel features without pulverizing the primitive relationship between channels. As we all know, the relationship of pixels in an image is identified with the distances among pixels, hence we can infer that the relationship between channel features is additionally equivalent: the great dependence can be found between the adjacent channels, and the dependence relationship is gradually decreasing with the increasing distance of channels. Moreover, Ref. [20] also revealed that the trend of frequency in different images is fundamentally similar in the same convolutional layer, and expresses a robust local periodicity. Therefore, correlation calculations are only performed on the adjacent \(k\) channels are in the ACAB. As shown in Figure 5, ACAB is composed of a global average pooling layer, the nearest neighbor fully connected module, and a channel feature representation layer. Here, the nearest neighbor fully connected module only connects the k nearest channels to investigate the relationship between channels. Figure 4: wRU module, the wSE module is used to generate weight values for different features. Based on the above-mentioned analysis, we can roughly get the channel attention weight of the whole image by exploring the relationship between adjacent \(k\) channels. The weight of the \(i\)-th channel \(y_{i}\) of the feature \(\mathbf{y}\) can be acquired as follows:  
\[w_{i}=\delta\left(\sum_{j=1}^{k}\alpha_{i}^{j}y_{i}^{j}\right),y_{i}^{j}\in \Omega_{i}^{k}, \tag{12}\]  
where \(\delta\) represents the Sigmoid activation function, \(\alpha_{i}^{j}\) represents the parameter of the convolution kernel corresponding to \(y_{i}\), and \(\Omega_{i}^{k}\) represents the set of \(k\) adjacent channels of \(y_{i}\). To further boost the super-resolution performance, all channels share weight information, and then the amount of parameters can be reduced to \(k\times C\), as:  
\[w_{i}=\delta\left(\sum_{j=1}^{k}\alpha^{j}y_{i}^{j}\right),y_{i}^{j}\in \Omega_{i}^{k}, \tag{13}\]  
where \(C\) is the channel number. Since the adaptive channel attention is to fittingly obtain cross-channel information, it is incredibly necessary to determine the range of channel interaction \(k\).