## 2 Materials and Methods
### Space and Channel Reconstruction Convolution (SCConv)
#### 2.2.2 Channel Reconstruction Unit (CRU)  
The structure of the channel reconstruction unit, CRU, is shown in Figure 4. CRU consists of three parts: segmentation, transformation, and fusion. The rich representative features in the channel are extracted by segmenting the channel in the feature map and using the efficient convolution operation as well as reusing features. Split: A spatially refined feature \(X^{w}\in R^{c\times h\times w}\) is received, and the spatially refined feature \(X^{w}\) is first split into two parts: channel \(\alpha C\) and channel \((1-\alpha)C\), as shown in the split part of Figure 4, where \(0\leq\alpha\leq 1\) is the split ratio. Then, the number of channels of these two parts of the feature is further compressed using a \(1\times 1\) convolution kernel as a way to improve the computational efficiency. The spatially optimized feature \(X^{w}\) is divided into the upper part \(X_{up}\) and the lower part \(X_{low}\) by performing the split and compression operations. Transform: A transform operation is performed on the compressed features, and the upper half of \(X_{up}\) is fed into the upper transform stage as a \"rich feature extractor\". In this stage, efficient convolution operations, group-wise convolution (GWC), and point-wise convolution (PWC) are used instead of the expensive standard \(k\times k\) convolution in order  
Figure 4: CRU structure diagram. to extract high-level representative information and reduce computational cost. Although GWC reduces the parameters and the computation cost, it also cuts off the information flow between different channel groups, so another path uses PWC to help the information flow across channels. So, the \(k\times k\) GWC operation and the \(1\times 1\) PWC operation are performed on the same \(X_{up}\), respectively. Finally, the outputs are summed to form the merged representative feature map \(Y_{1}\), as shown in the transform section of Figure 4. The upper transform stage can be expressed in Equation (5):  
\[Y_{1}=M^{\text{G}}X_{up}+M^{\text{P}_{1}}X_{up} \tag{5}\]  
where \(M^{\text{G}}\in R^{\frac{\text{G}}{\text{WP}}\times k\times k\times c},M^{ \text{P}_{1}}\in R^{\frac{\text{G}}{\text{WP}}\times 1\times 1\times c}\) are the learnable weight matrices of GWC and PWC, respectively, and \(X_{up}\in R^{\frac{\text{G}}{\text{WP}}\times h\times w}\) and \(Y_{1}\in R^{c\times h\times w}\) are the upper input and output feature maps, respectively. In short, the upper transformation stage utilizes the outputs of GWC and PWC on the same feature maps \(X_{up}\) to form \(Y_{1}\), which is used to extract rich representative information while reducing the computational cost. The second half of \(X_{low}\) is fed into the lower transformation stage. In this stage, a cheap \(1\times 1\) PWC operation is used to generate feature maps with shallow hidden details as a \"complement to the rich feature extractor (detail information)\". In addition, reusing \(X_{low}\) yields more feature maps without additional computational cost. Finally, the generated and reused feature maps are merged to form the output \(Y_{2}\) as shown in Equation (6):  
\[Y_{2}=M^{\text{P}_{2}}X_{low}\cup X_{low} \tag{6}\]  
where \(M^{\text{P}_{2}}\in R^{\frac{(1-\text{s})\text{C}}{r}\times 1\times 1\times(1- \frac{(1-\text{s})}{r})^{\text{C}}}\) is the learnable weight matrices of the PWC, \(\cup\) is the cascade operation, and \(X_{low}\in R^{\frac{(1-\text{s})\text{C}}{r}\times h\times w}\) and \(Y_{2}\in R^{c\times h\times w}\) are the lower input and output feature maps, respectively. In short, the lower transformation stage reuses the feed-forward feature map \(X_{low}\) and utilizes the \(1\times 1\) PWC operation as a complement to the rich feature extractor and then joins them to form feature \(Y_{2}\) with complementary detail information.