## 2 Materials and Methods
### Method
#### 2.2.1 Noise Suppression Module  
Speckle noise is a complex physical characteristic observed in ultrasound images that frequently poses challenges in accurate object localization. The adoption of frequency representation presents a novel approach to discerning differences between categories, potentially revealing insights overlooked by human visual perception. To mitigate this, we propose a Noise Suppression Module (NSM) that considers speckle noise suppression from a frequency perspective, as illustrated in Figure 4.  
**Low-pass filter (LPF).** Low-frequency components occupy most of the energy in the absolute image and represent most of the semantic information. A low-pass filter allows signals below the cutoff frequency to pass, while signals above the cutoff frequency are obstructed. Thus, we employed typical average pooling as a low-pass filter. However, the cutoff frequencies of different images are different. To adapt to this, we utilized channel splitting [20], where the feature map is partitioned into multiple groups. This allowed us to apply different kernels and strides to each group, thereby generating low-pass filters. For the \(m\)th group, we have  
\[LPF_{m}(v^{m})=Up(\Gamma_{s\times s}(v^{m})), \tag{1}\]  
Figure 4: Overall architecture of NSM. It is composed of a low-pass filter (LPF) and a high-pass filter (HPF).  
where \(Up(\cdot)\) represents upsampling, \(\Gamma_{s\times s}\) denotes the adaptive average pooling with the output size of \(s\times s\), \(s\in\{1,2,3,6\}\), and \(v^{m}\) stands for the \(m\)th channel split from the input feature map, \(m\in\{1,2,3,4\}\).  
**High-pass filter (HPF).** High-frequency information is crucial to preserve details in segmentation. As a typical high-pass operator, convolution can filter out irrelevant low-frequency redundant components to retain favorable high-frequency components. The high-frequency components determine the image quality, and the cutoff frequency of the high pass for each image is different. Similar to the LPF, we partitioned the feature map into \(n\) groups. For each group, we used a convolution layer with different kernels to simulate the cutoff frequencies in different high-pass filters. For the \(n\)th group, we have  
\[HPF_{n}(v^{n})=\Lambda_{k\times k}(v^{n}), \tag{2}\]  
where \(\Lambda_{k\times k}\) denotes the depthwise convolution layer with a kernel size of \(k\times k\), \(k\in\{1,3,5,7\}\), and \(v^{n}\) stands for the \(n\)th channel split from the input feature map, \(n\in\{1,2,3,4\}\). The continuous accumulation of speckle noise within the internal high frequencies often yields adverse effects on the extracted high-frequency information. Therefore, we employed Gaussian filtering on the high-frequency features to effectively eliminate noise.  
\[W(x,y)=\frac{1}{2\pi\sigma^{2}}e^{-\frac{y^{2}+y^{2}}{2\sigma^{2}}}, \tag{3}\]  
\[G(x,y)=\sum_{i=0}^{k}\sum_{j=0}^{k}W(i,j)\cdot I(x+i,y+j), \tag{4}\]  
where \(W(x,y)\) represents the Gaussian weight matrix and \(\sigma\) is the standard deviation of the Gaussian function. \(G(x,y)\) represents the value of the Gaussian function at the spatial coordinates \((x,y)\), \(k\) stands for the window size of the Gaussian filter, and \(I\) represents the high-frequency feature by the pooling filter. The final output, \(F_{NSM}\), is obtained by summing the denoised high-frequency information with the low-frequency information:  
\[F_{NSM}=[HPF_{n}(v^{n})]+G([LPF_{n}(v^{n})]), \tag{5}\]  
where \([\cdot]\) indicates the concatenate operation, which integrates feature maps of different cutoff frequencies.