## 3 Proposed Method
### Network Structure  
#### 3.2.1 ConvNeXt-SimAM Branch  
To fully extract the local detail features of SAR vehicle targets, we constructed the ConvNeXt-SimAM branch by stacking CNN blocks and down-sampling operations, and the whole branch is divided into three stages, as shown in Figure 1. To align with the size of the feature map of each stage in the Swin Transformer branch, the height and width of the feature map of each stage in the ConvNeXt-SimAM branch are reduced by half of the previous stage through a down-sampling convolution operation, while doubling the number of channels. Moreover, the shallow local fine-grained and deep coarse-grained information from stage 1 and stage 3, respectively, are extracted and sent to the multi-scale feature fusion branch, which can fuse local features of different scales to enhance the feature representation ability of the model. The CNN block architecture is shown in Figure 2a. Inspired by ConvNeXt, the CNN block comprises a sequence of group convolutions with a convolution kernel size of 7 \(\times\) 7, layer normalization (LN), convolutions with a kernel size of 1 \(\times\) 1, GELU activation functions, SimAM attention modules, and convolutions with a convolution kernel size of 1 \(\times\) 1. To introduce additional learnable parameters, we inserted the SimAM [28] attention module after the second convolutional layer (conv k1,\(A\)\(\times\) dim) of the CNN block, enhancing the local feature extraction ability of the CNN block to fully extract SAR vehicle detail features and to suppress speck noise. Unlike the existing channel attention or spatial attention mechanisms, the SimAM module can derive three-dimensional attention weights from the feature maps of channels and spatial dimensions without adding additional parameters, which flexibly and effectively enhances the representation ability of convolutional modules. [PERSON] et al. [29] defined an energy function for each neuron on the feature map based on the discovery of neurology, and the input feature was \(X\in\mathbb{R}^{C\times H\times W}\), so each channel had \(H\times W\) energy functions. The importance of each neuron was evaluated by minimizing the energy function, and higher weight was given to neurons with a greater influence, thus enhancing the ability to extract local features and effectively suppressing noise interference. Therefore, the formula after minimizing the energy function is shown in Equation (1):  
\[e_{t}^{*}=\frac{4(\sigma^{2}+\lambda)}{\left(t-\mu\right)^{2}+2\sigma^{2}+2\lambda} \tag{1}\]  
where \(t\) is the target neuron in a single channel of \(X\), that is, the pixel value; \(\mu\) and \(\sigma\) are the mean and variance of pixel values of all neurons on the channel feature map,  
Figure 1: The structure diagram of the MFN model. (The green section represents the Swin Transformer branch. The blue section represents the CovNeXt-SimAM branch. The yellow part represents the multi-scale feature fusion branch.) respectively; and \(\lambda\) is the regularization coefficient. The lower the energy of neuron \(t\), the higher its importance. The final output of input feature \(X\) after the SimAM attention mechanism is as follows:  
\[\widetilde{X}=sigmoid(\frac{1}{E})\otimes X \tag{2}\]  
where \(E\) groups all \(e_{t}^{*}\) across the channel and spatial dimensions, and \(\otimes\) represents element-wise multiplication [30]. In the ConvNeXt block, group convolution \(f^{d\gamma\times 7}\) with a convolution kernel size of \(7\times 7\) and a channel number of dim is performed first, where the number of groups is equal to the number of channels. The use of group convolution can reduce the calculation amount of the model. Subsequently, layer normalization is used, and the convolution operation \(f^{1\times 1}\) with a convolution kernel size of \(1\times 1\) and a channel number of \(4\times\) dim is used to upgrade the dimension.