## 2 Relevant Theory
### Attention-Based Multi-Channel Feature Refinement Module Enhanced by Dilated Convolution  
Due to the harsh conditions of underground coal mine environments, the acquired coal-rock images often contain a considerable amount of noise. As the depth of the network increases, some of this noise tends to persist within certain channels, ultimately impairing the accuracy of the final segmentation results. Feature selection is facilitated by an intermediate attention mechanism, which is inserted between the encoder and decoder to mitigate noise impact and improve discriminative representation learning. Specifically, a channel-wise attention module (SEBlock) is employed to automatically evaluate the importance of each channel. By adaptively adjusting channel weights, the network enhances the extraction of meaningful features while suppressing irrelevant or noisy information.  
First, the SEBlock uses global pooling to compress the feature map of each channel into a single real number that represents the global feature information. The formula is as follows.  
\[X_{c}=\frac{1}{W\times H}\sum_{i=1}^{W}\sum_{j=1}^{H}x_{(i,j)} \tag{3}\]  
The variables \(W\) and \(H\) represent the spatial dimensions--width and height--of the feature map, while \(x_{(i,j)}\) indicates the pixel intensity value at position \((i,j)\).  
ReLU activation is applied to the global features, followed by sigmoid gating to generate the attention weight \(S_{c}\) within the range \([0,1]\). The equation is shown below.  
\[S_{c}=\sigma(W_{2}\delta(W_{1}X_{c})) \tag{4}\]  
In this context, \(\delta(\cdot)\) denotes the ReLU activation function, and \(\sigma(\cdot)\) stands for the Sigmoid activation function. The symbols \(W_{1}\) and \(W_{2}\) refer to two fully connected layers positioned prior to these activation functions. Specifically, the first layer reduces the number of global feature channels to one-sixteenth of the original size, and the second restores it back to its initial dimensionality. This compression-expansion structure helps  
Figure 6: Res2 Bolck module.  
reduce computational complexity while facilitating the integration of information across different channels.  
Finally, the attention mechanism's feature vector is multiplied by the original feature map along the channel dimension. To prevent information loss, a residual structure is used to add the original feature map to the result. The calculation formula is as follows.  
\[F_{c}=X_{c}(1+S_{c}) \tag{5}\]  
Thus, the residual attention structure is constructed, as shown in Figure 7.  
While the SEBlock is effective in capturing globally salient features, it exhibits limitations in mitigating localized noise interference. Additionally, its global feature suppression strategy may unintentionally eliminate informative details that are essential for accurate representation. To overcome these shortcomings, we propose a multi-channel residual attention module that integrates dilated convolution. This module is specifically designed to attenuate fine-grained noise while preserving crucial feature representations across multiple spatial scales. The structure of the proposed module is shown in Figure 8.  
In this paper, a three-branch parallel structure is employed to construct the attention mechanism at multiple observation scales. Specifically, it consists of a \(1\times 1\) convolution, a \(3\times 3\) dilated convolution with a dilation rate of 2, and a \(3\times 3\) dilated convolution with a dilation rate of 4. This configuration enables the network to capture attention features at different receptive field sizes, thereby effectively suppressing diverse types of noise signals. By integrating dilated convolutions with varying dilation rates, the proposed multi-channel residual attention module suppresses ineffective information across multiple scales, reduces noise interference, and enhances the representation of salient features. Furthermore, the inclusion of a residual connection helps preserve shallow feature information, which improves both the accuracy and robustness of the model.