## 2 Materials and Methods
### Improved Network Module
#### 2.2.2 Frequency Band Feature Separator (FBFS)  
To introduce frequency domain information, a Frequency Band Feature Separator (Figure 3) module is designed. This module first employs pointwise convolution to enhance the nonlinearity of features, generating new features with unchanged dimensions. It then utilizes the Haar wavelet transform to decompose frequency domain features into horizontal, vertical, and diagonal high-frequency components, as well as a low-frequency component. The three high-frequency components are concated, and pointwise convolutions and batch normalization are applied separately to obtain high-frequency and low-frequency features embedded in the CNN network. The FBFS module leverages the simplicity and efficiency of the Haar wavelet transform for image signal decomposition to effectively extract frequency domain features, enabling more comprehensive feature representation.  
For the input \(X\in R^{C\times H\times W}\), a pointwise convolution operation is first performed to enhance feature nonlinearity, resulting in a new feature \(X\in R^{C\times H\times W}\) with unchanged dimensions. A first-order Haar wavelet transform is applied to each channel of \(X_{c}\in R^{H\times W}\).  
\[\begin{cases}A_{c}(i,j)=\frac{X_{c}(i2j-1)+X_{c}(i,2j)}{2}\\ \\ D_{c}(i,j)=X_{c}(2i-1,j)-X_{c}(2i,j)\end{cases} \tag{2}\]  
Here, \(A_{c}(i,j)\) represents the low-frequency approximation coefficients of channel \(c\), \(D_{c}(i,j)\) represents the high-frequency detail coefficients of channel \(c\), where \(i\) is the row index and \(j\) is the column index. After the first-order Haar wavelet transform, the width of each row is halved, and the range of \(j\) changes from 1 to \(\frac{W}{2}\). Subsequently, the following Haar wavelet transform is applied to each column of the low-frequency approximation coefficients \(A_{c}(i,j)\) and high-frequency detail coefficients \(D_{c}(i,j)\) of channel \(c\):  
Figure 3: Frequency Band Feature Separator.  
Figure 2: Atrous Bottleneck Pyramid Module (ABPM).  
\[\begin{cases}A_{c}=AA_{c}(i,j)=\frac{A_{c}(i(2j-1)+A_{c}(i(2j))}{2}\\ H_{c}=AD_{c}(i,j)=\frac{D_{c}(i(2j-1)-D_{c}(i(2j))}{2}\\ V_{c}=DA_{c}(i,j)=A_{c}(i,2j-1)-A_{c}(i,2j)\\ D_{c}=DD_{c}(i,j)=D_{c}(i,2j-1)-D_{c}(i,2j)\end{cases} \tag{3}\]  
Here, \(A_{c}\) represents the approximation coefficients of a single channel, \(H_{c}\) represents the horizontal detail coefficients of a single channel, \(V_{c}\) represents the vertical detail coefficients of a single channel, and \(D_{c}\) represents the diagonal detail coefficients of a single channel. The coefficients \(H_{c}\), \(V_{c}\), and \(D_{c}\) are combined into high-frequency components, while \(A_{c}\) represents the low-frequency component. Both the high-frequency and low-frequency components are subjected to \(1\times 1\) convolution for low-dimensional mapping and batch normalization, resulting in high-frequency and low-frequency features:  
\[F_{l},F_{h}=(\psi(\delta_{1\times 1}(A)),\psi(\delta_{1\times 1}(Cat(H,V,D)))) \tag{4}\]  
Here, \(\delta_{1\times 1}()\) represents the \(1\times 1\) convolution, \(\psi()\) represents batch normalization, and \(F_{l},F_{h}\in(C,H/2,W/2)\) represent the low-frequency and high-frequency features, respectively.