## 2 Relevant Theory
### Multi-Scale Brightness-Enhancement Module  
The multi-scale brightness-enhancement module proposed in this paper is inspired by the Pyramid Scene Parsing Network (PSPNet), introduced by [PERSON] et al. in 2016 [22]. In their work, the authors proposed a pyramid pooling module (PPM), which integrates multiple receptive fields by performing pooling operations on regions of varying sizes and strides. Feature maps from different receptive field scales are then fused through upsampling, concatenation, and convolution operations. Although the pooling layer effectively enlarges the receptive field, it may result in significant information loss, leading to blurred boundaries and color inconsistencies in the enhanced image. To address this issue, we propose a multi-scale brightness-enhancement module based on hybrid dilated convolution (Figure 4), which increases the receptive field while mitigating the loss of critical feature information.  
Figure 3: NR-Transformer for denoising networks. (**a**) The reflectivity denoising module, (**b**) the Transformer body structure, and (**c**) the multiple attention mechanism.  
Hybrid dilated convolution enables a more effective preservation of pixel-level information across different spatial locations in the feature map by superimposing dilated convolutions with varying dilation rates. Without increasing the number of parameters, this design retains more fine-grained details from the original feature map and reduces the likelihood of local enhancement artifacts during brightness adjustment. The proposed multi-scale brightness-enhancement module aggregates feature information from four different receptive fields to perform adaptive brightness enhancement across multiple spatial scales, thereby addressing the issue of non-uniform illumination commonly found in coal-rock images. Specifically, the first convolutional branch employs three consecutive standard convolutional layers with \(3\times 3\) kernels, resulting in an effective receptive field size of 7. The second branch consists of one \(3\times 3\) dilated convolution with a dilation rate of 2, followed by two standard \(3\times 3\) convolutions, yielding a receptive field of 9. The third branch includes three \(3\times 3\) dilated convolutions with dilation rates of 2 and 3, along with one standard convolution, resulting in a receptive field of 13. The fourth branch utilizes three \(3\times 3\) dilated convolutions with dilation rates of 2, 3, and 4, achieving a receptive field size of 19. The resulting feature maps from all branches are fused via a convolutional layer to construct the final multi-scale luminance enhancement module.  
The dilation rates (2, 3, and 4) adopted in the proposed module were determined through empirical analysis and limited grid-based experimentation. Preliminary tests showed that smaller dilation rates (e.g., 1) failed to provide adequate receptive field coverage, leading to insufficient context aggregation in uneven lighting conditions. Conversely, larger dilation rates (e.g., 5 or above) introduced aliasing artifacts and degraded boundary sensitivity. Therefore, dilation rates of 2, 3, and 4 were selected as a balanced configuration that effectively captures multi-scale contextual information while maintaining structural coherence and computational efficiency.