## 3 Methods
### Decoder
#### 3.3.2 Feature Refinement Module  
Due to the imaging mechanism of SAR, noise is inevitably present in the images, which significantly complicates feature processing. A common method to suppress noise interference is the integration of attention mechanisms into the network. The core idea is to automatically assign different weights to features, assigning higher weights to target features and lower weights to noise, thereby reducing interference. However, when the distribution of noise and target features is similar, directly applying attention mechanisms may not accurately distinguish between noise and target features. To minimize the potential impact of noise, we designed a feature refinement module (FRM) that applies weighting to different features within a local scope, allowing the network to focus more precisely on the target features, as shown in Figure 5.  
Figure 4: The structure of hierarchical decoder.  
Figure 5: The structure of feature refinement module.  
Given an input feature map, we divided it into three sub-feature maps \(F^{(t)}\), where \(t=1,2,3\) correspond to the three sub-features, respectively. Next, we applied the CBAM [26] to \(F^{(t)}\). The CBAM includes both a channel attention module (CAM) and a spatial attention module (SAM), which collaboratively enhance feature representations across both the channel and spatial domains. Specifically, \(F^{(t)}\) was processed through max pooling and average pooling layers, generating two separate outputs. These outputs were then passed through a shared multi-layer perceptron (MLP), and their outcomes were summed. Next, the summed results were processed through a Sigmoid function to output the channel attention weights \(M_{\text{C}}^{(t)}\). Mathematically,  
\[M_{\text{C}}^{(t)}=\sigma(MLP(AvgPool(F^{(t)})+MLP(MaxPool(F^{(t)}) \tag{7}\]  
where \(\sigma(\cdot)\) denotes the Sigmoid function, and \(MaxPool(\cdot)\) and \(AvgPool(\cdot)\) denote the max pooling and average pooling operations, respectively.  
\(M_{\text{C}}^{(t)}\) are multiplied by \(F^{(t)}\) to generate the channel-wise refined feature map \(F_{\text{C}}^{(t)}\). Mathematically,  
\[F_{\text{C}}^{(t)}=F^{(t)}\otimes M_{\text{C}}^{(t)} \tag{8}\]  
where \(\otimes\) means element-wise multiplication.  
After channel refinement, \(F_{\text{C}}^{(t)}\) is further refined in the spatial domain through the SAM. \(F_{\text{C}}^{(t)}\) is processed using both max pooling and average pooling, and the outputs of each pooling process are concatenated. The concatenated feature map is passed through a \(7\times 7\) convolutional layer, followed by a Sigmoid function to output the spatial attention weights \(M_{S}^{(t)}\). Mathematically,  
\[M_{S}^{(t)}=\sigma(f^{7\times 7}([MaxPool(F_{\text{C}}^{(t)}),AvgPool(F_{\text{C}}^ {(t)})])) \tag{9}\]  
where \(f^{7\times 7}(\cdot)\) denotes the computation using a \(7\times 7\) convolution kernel.  
\(M_{S}^{(t)}\) are multiplied by \(F_{\text{C}}^{(t)}\) to generate the spatial-wise refined feature map \(F_{S}^{(t)}\). Mathematically,  
\[F_{S}^{(t)}=F_{\text{C}}^{(t)}\otimes M_{S}^{(t)} \tag{10}\]  
Finally, each enhanced sub-feature map is concatenated to form the final output \(F^{\prime}\). Mathematically,  
\[F^{\prime}=C(F_{S}^{(1)},F_{S}^{(2)},F_{S}^{(3)}) \tag{11}\]