## 3 Methodology
### C3k2-PRFE Module  
PCB images are characterized by densely packed components, intricate wiring, and diverse textures with substantial background interference. Expanding the receptive field allows the model to capture richer contextual information, thereby enhancing the defect-background discrimination and reducing false detections [33]. Inspired by TridentNet, the RFE [34] module employs four parallel dilated convolutional branches with varying dilation rates to extract multi-scale features. Each branch covers a distinct receptive field, which improves feature representation while minimizing parameters and overfitting risk. Building upon this, an improved receptive field enhancement module, named PRFE, is presented. By replacing the C3k module in C3k2 with PRFE, a novel feature extraction module termed C3k2-PRFE is constructed. The PRFE module effectively enhances feature extraction through innovative preprocessing techniques. First, a 1 \(\times\) 1 point-wise convolution expands input channels, projecting low-dimensional features into a high-dimensional space to enhance the non-linear expressive capacity. Subsequently, depthwise separable 3 \(\times\) 3 convolutions are applied to extract spatial features, executing an initial fusion of local context features on the input. The step suppresses pixel-level interference at small target boundaries. The 3 \(\times\) 3 convolution operation performs smoothing on input features through weighted averaging, effectively suppressing high-frequency interference, thereby reducing pixel-level noise at small target edges. Meanwhile, the output features of the 3 \(\times\) 3 convolution contain local structural information, providing a clearer semantic foundation for subsequent multi-scale dilated convolution operations. The formula for calculating the output features of 3 \(\times\) 3 convolution is as follows:  
\[Z_{i,j,c}=\sum_{m=-1}^{1}\sum_{n=-1}^{1}w_{m,n}\cdot x_{i+m,j+n,c}+b_{c}, \tag{1}\]  
where \(Z_{i,j,c}\) represents the feature value of the output feature map at position (\(i\),\(j\)) in channel \(c\); \(x_{i+m,j+n,c}\) denotes the original value of the input feature map at position (\(i+m,j+n\)) in channel \(c\), which may contain pixel-level noise; \(w_{m,n}\) denotes the weight parameters of the 3 \(\times\) 3 convolution kernel at offset (\(m\),\(n\)); and \(b_{c}\) denotes the bias term of channel \(c\). Then, subsequent receptive field enhancement operations are performed on cleaner, more semantically distinct features while also pre-augmenting local small-target characteristics, thus mitigating excessive detail attenuation caused by enlarged receptive fields. The preprocessed features are then split into three parallel branches, each of which undergoes dimensionality expansion via 1 \(\times\) 1 convolutions. These branches employ 3 \(\times\) 3 dilated convolutions with dilation rates (d = 1, 2, 3), respectively, to capture multi-scale contextual information, forming hierarchical receptive field combinations. After the branch outputs are reduced in dimensionality through 1 \(\times\) 1 convolutions, they are concatenated in a residual manner. The fused features are then summed with the original input to retain low-level de tails and mitigate gradient vanishing. During the fusion process, global average pooling is utilized to generate channel-wise weight coefficients, which are normalized and multiplied by branch features to dynamically prioritize channels. The weighted features are integrated across channels to produce multi-scale enhanced features. Finally, a \(1\times 1\) convolution adjusts the number of channels, which combines with secondary residual connections to ensure the retention of multi-scale critical information. The framework of the PRFE module is displayed in Figure 2.  
In summary, the PRFE module is constructed by incorporating a \(3\times 3\) convolution preprocessing with the RFE module for feature refinement. This stage extracts initial local features while suppressing high-frequency interference.