# Gradient-Guided and Multi-Scale Feature Network for Image Super-Resolution
## 3 Proposed Network
### Multi-Scale Convolution Unit  
To improve the feature representation ability of the network, a common method is to design a very deep network with tremendous convolutional layers to explore more abundant features. Although this method can improve network performance to a certain extent, it also brings other problems. On the one hand, the extending of the network depth is accompanied by a continuous expansion in the number of parameters, which may prompt overfitting in the case of inadequate training data. On the other hand, a network with an incredible number of layers implies higher computational complexity and is prone to bring in gradient exploding or vanishing, making network optimization difficult. Fortunately, the GoogLeNet [41] model solves these problems well. The critical thought of the Inception is to build a dense block structure. It utilizes multi-scale convolution kernels to acquire the feature map, and then combines the output of several branches to the following layer. The structure accelerates both the qualities and the resilience to scale without increasing the network depth of the network, thus improving the capability of feature extraction. For the RIB structure, different from the original Inception module, we removed the pooling layer. Since the max-pooling operation extracts the maximum value of the feature map in a certain area to generate the representative salient features in the area, which may result in the loss of a large amount of detail features. Thus, the pooling operation is often fatal for SR tasks. For example, a \(3\times 3\) max-pooling operation may cause the feature map to losing nearly 8/9 of the important information. For low-level tasks such as image super-resolution, the feature information of each pixel is very important. Consequently, we directly use the stepping convolutional layer to replace the pooling layer. For the SR task, we propose a multi-scale convolution unit with a parallel structure to extract the receptive field features of different scales to recover as many image detailsas possible. Specifically, we first assemble convolution filters of various scales into the network, such as \(1\times 1\), \(3\times 3\), \(5\times 5\). However, a larger-scale convolution kernel incurs higher computational costs and increases the time complexity. Consequently, in our network, we use small-scale filters instead of large-scale ones to minimize the number of parameters [42; 43]. In fact, in our network, only \(1\times 1\) and \(3\times 3\) scale convolution filters are used, and the \(5\times 5\) scale filter is replaced by two cascaded \(3\times 3\) scale filters. Ref. [42] has proved that the features extracted by filters with a scale larger than \(3\times 3\) are typically weak as the filter with a scale larger than \(3\times 3\) can generally be simplified to a set of filters with a scale of \(3\times 3\), and the parameter of two cascaded \(3\times 3\) scale filters is only \(18/25\) of the parameter of a single \(5\times 5\) scale filter. As shown in Figure 2a, our RIB (Residual Inception Block) employs the multi-branch structure with different scale convolution kernels to correspond to different sizes of receptive fields, and the scales of the convolution kernel on the three branches are \(1\times 1\), \(1\times 1\) and \(3\times 3\), \(1\times 1\) and a set of cascaded \(3\times 3\), respectively. In this way, more features could be learned, and then the features of the three branches are fused to obtain the representative feature. In addition, Ref. [42] also proved that asymmetric convolution kernels [44] could be used to replace conventional symmetric convolution kernels. In certain situations, asymmetric convolution kernels can learn more representative features than symmetric convolution kernels, and reduce computational complexity without loss of accuracy.