# OmniSR-M: A Rock Sheet with a Multi-Branch Structure Image Super-Resolution Lightweight Method
## 2 Materials and Methods
### Multi-Branch Structure  
In order to make the OSAG module more lightweight and efficient while retaining the multi-scale feature information, this paper proposes the omni-scale aggregation group (OSAG) with multi-branching structure, which firstly extracts the image features using the shallow feature extraction network layers Net64, Net32, and Net16, respectively, with 64, 32, and 16 being the number of feature channels outputted from each network. The first branch is Net64, which mainly retains global semantic information, and this branch handles 64-channel feature maps. The second branch is Net32, which is responsible for aggregating local region information, and this branch processes 32-channel feature maps. The third branch is Net16, which is used to learn local details, and this branch handles 16-channel feature maps. Three branches are operated in parallel for deep feature extraction, using residual structures to splice the original shallow features and the deep features extracted through the OSAG module. Inverse convolution usually refers to transposed convolution, also known as fractional step convolution or upsampling convolution, which is a commonly used upsampling method, the principle of which is shown in Figure 3[23; 24]. In this paper, this approach is used to resize the feature map in order to fuse features of different scales to form a multi-scale feature output containing global to local features. Such a design in this paper takes full advantage of the idea of extracting multi-scale features in parallel with multiple lightweight sub-networks, which retains the multi-scale modeling capability of OSAG and improves the computational efficiency, making the OSAG module more suitable for use in lightweight and speed-critical scenarios.  
Specifically, the shallow features of the image are first extracted using a multilayer \(3\times 3\) convolutional kernel, and the output feature maps are of different sizes, \(64\times H\times W\), \(32\times H\times W\), and \(16\times H\times W\), respectively. Then, the deep features on different scales are extracted separately by the OSAG module, the residual structure fuses the original shallow features, and finally, the features are fused using the inverse convolution operation. This process can be described as follows:  
\[F_{64}=Conv3\times 3(X) \tag{16}\]  
\[F_{32}=Conv3\times 3(X) \tag{17}\]\[F_{16}=Conv3\times 3(X) \tag{18}\]  
where \(X\) is the input image and \(F_{64}\), \(F_{32}\) and \(F_{16}\) denote the 64-channel, 32-channel, and 16-channel feature maps, respectively.  
\[F_{64}^{\prime}=OSAG(F_{64})+F_{64} \tag{19}\]  
\[F_{32}^{\prime}=OSAG(F_{32})+F_{32} \tag{20}\]  
\[F_{16}^{\prime}=OSAG(F_{16})+F_{16} \tag{21}\]  
\[F_{fusion}=Conv_{1\times 1}\big{(}F_{64}^{\prime},C\big{)}+Conv_{1\times 1}\big{(} F_{32}^{\prime},C\big{)}+Conv_{1\times 1}\big{(}F_{16}^{\prime},C\big{)} \tag{22}\]  
where, \(F_{64}\), \(F_{32}\), \(F_{16}\) are the feature maps extracted by the shallow network; \(F_{64}^{\prime}\), \(F_{32}^{\prime}\), \(F_{16}^{\prime}\) are the deep features extracted by OSAG module; \(Conv_{1\times 1}\) is the \(1\times 1\) convolution, which is mainly used for adjusting the number of channels; and C is the number of required channels.  
In summary, the design of OSAG modules with a multi-branch structure proposed in this paper not only improves the richness of feature representations but also makes significant progress in terms of light weight and efficiency.