# HIEN: A Hybrid Interaction Enhanced Network for Horse Iris Super-Resolution
## 2 Materials and Methods
### Shallow Feature-Extraction Module
#### 2.2.4 Efficient Residual Dense Block  
For powerful local feature extraction, deep and complex modules are effective but often come at a high computational cost. To address this trade-off, we introduce the Efficient Residual Dense Block (ERDB), our primary module for local feature learning, shown in Figure 7.  
The design of the ERDB integrates two key principles. First, it uses the proven structure of residual dense connectivity to encourage feature reuse and robust gradient flow. Second, and most critically for efficiency, it replaces standard convolutions with depthwise separable convolutions. This choice is fundamental to creating a lightweight yet powerful feature extractor.  
Depthwise separable convolutions work by factorizing a standard convolution into two distinct, simpler steps: a depthwise step and a pointwise step. This factorization drastically reduces both the parameter count and the computational load (FLOPs) [28]. The key advantage of this efficiency is that it allows us to build a more powerful network overall; we can construct deeper or more complex local modules without incurring prohibitive computational costs. Our approach aligns with a broader, successful trend in the field toward designing lightweight yet effective architectures. For instance, [PERSON] et al. recently demonstrated this philosophy by combining lightweight Ghost modules with attention mechanisms for efficient medical image segmentation [29], validating the power of this design direction.  
The ERDB is built from a basic convolutional unit, denoted ERDB_Conv. Given an input feature map \(x\in\mathbb{R}^{h\times m\times c}\), this operation can be formulated as:  
\[\hat{x}=\text{PWConv}_{1\times 1}(\text{DWConv}_{3\times 3}(x)), \tag{8}\] \[F_{\text{ERDB\_Conv}}=\text{Concat}(\text{GELU}(\hat{x}),\ x),\]  
Figure 7: The illustration of the LFEM. (**a**) Local Feature-Extraction Module. (**b**) The Efficient Residual Dense Block (ERDB) is used to extract local features from the image.  
where DWConv3 \(\times\) 3(\(\cdot\)), PWConv1 \(\times\) 1(\(\cdot\)), GELU(\(\cdot\)), and Concat(\(a,b\)) represent the depth-wise convolution, point-wise convolution, GELU activation, and the channel-wise concatenation of tensors \(a\) and \(b\), respectively. The ERDB is composed of multiple convolutional units with local feature fusion and residual connections. Given an input feature map \(x\in\mathbb{R}^{h\times w\times c}\), the process can be expressed as:  
\[\begin{split} x_{0}&=x,\\ x_{c}&=F_{\text{ERDB\_Conv}}^{(c)}(x_{c-1}),\quad c=1,2,\ldots,C,\\ F_{\text{ERDB}}&=H_{\text{LFF}}(x_{c})+x,\end{split} \tag{9}\]  
where \(C\) denotes the number of stacked ERDB_Conv blocks, and \(H_{\text{LFF}}(\cdot)\) represents the local feature fusion operation implemented using a \(1\times 1\) convolution.  
The key of the ERDB_Conv unit lies in its residual dense connection pattern. Rather than passing each ERDB_Conv output directly to the next layer, we concatenate its output with its own input feature map. This dense connectivity ensures that every layer can aggregate information from all preceding units, achieving deep feature fusion and reuse.