## 2 The Proposed Method
### Multi-Scale Attention-Coupling Feature-Enhancement Mechanism  
The issue of feature loss during the encoder's down sampling process, which worsens discrepancies between the reconstructed image and the original, this study proposes a multi-scale attention-coupling feature-enhancement mechanism. The proposed MSAC is designed to enhance the processing of semantic information across different depths and improve the representation of target features by integrating multi-scale features from various encoder layers, as illustrated in Figure 3.  
Figure 2: Architecture of the proposed network. The encoder extracts features from three distinct layers, denoted as E\({}_{1}\), E\({}_{2}\), and E\({}_{3}\), which are then processed by convolutional layers to produce feature maps of 128, 256, and 512 dimensions, respectively. The coordinate channel attention module captures inter-channel relationships and enhances feature representation. The feature maps generated by the coordinate channel attention module are then multiplied element-wise with the convolved encoder feature maps to refine feature representation. To unify the resolutions of the feature maps across different levels, they are upsampled to align their resolutions, followed by channel adjustment and element-wise summation to achieve multi-scale feature fusion. Finally, the fused feature maps are fed into different levels of the teacher generator to strengthen the model's capacity for capturing key features. To address the network's challenge of accurately detecting rail fastener anomalies in complex environments, this article designs a coordinate channel attention (CASE) mechanism that integrates positional and channel information. This CASE leverages the advantages of coordinate attention [45] and squeeze-and-excitation networks [46], enhancing spatial attention features and optimizing the weights of channel attention features. Embedding the CASE into the MSAC of the teacher network effectively enhances the representation of abnormal rail fastener parts and significantly improves detection accuracy. The structure of the module is shown in Figure 4.  
Given an input feature map \(X\) with dimensions \(C\times H\times W\), where \(C\) is the number of channels and \(H\) and \(W\) represent the height and width of the feature map, respectively. Firstly, average pooling is performed along the x-direction, followed by global average pooling along the height (\(h\)) dimension using Xavg, resulting in a \(C\times 1\times W\) feature map. The output expression is shown in Equation (1):  
\[z^{h}(j)=\frac{1}{H}\sum_{i=1}^{H}X_{c}(i,j),\ \forall j=1,2,\ldots,W \tag{1}\]  
Figure 4: Architecture of the coordinate channel attention module. Figure 3: Architecture of the multi-scale attention-coupling (MSAC) feature-enhancement mechanism. where \(X_{c}(i,j)\) represents the value at position \((i,j)\) in the \(C\)-th channel of the input feature map, and \(z^{h}(j)\) denotes the feature map obtained by applying global average pooling along the \(h\) dimension. Average pooling in the y-direction is performed by Yavg on the feature map \(Z\). Global average pooling is performed in the width (\(w\)) dimension to generate the \(C\times H\times 1\) feature map, and the width \(w\) output expression is shown in Equation (2):  
\[z^{w}(i)=\frac{1}{W}{\sum_{j=1}^{W}X_{c}(i,j)},\ \forall i=1,2,\ldots,H \tag{2}\]  
where \(z^{w}(i)\) represents feature map obtained by global average pooling along the \(w\)-dimensions. These two transformations integrate feature information from different spatial directions to generate a set of direction-aware feature maps, which can not only capture long-range dependencies in one direction, but also maintain the accuracy of rail fastener information in the other direction, which helps to improve the network's ability to detect abnormal parts.