## 4 Discussion  
Breast cancer is a prevalent gynecological disease which poses a significant threat to women's health. With the development of deep learning, intelligent analysis based on \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Backbone** & **mDice \(\uparrow\)** & **mIoU \(\uparrow\)** & \(MAE\)\(\downarrow\) \\ \hline UNet [18] & 0.7359 & 0.6395 & 0.8758 \\ Res2 Net [38] & 0.7641 & 0.6777 & 0.0413 \\ PVT (Ours) [22] & 0.8183 & 0.7350 & 0.0355 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Quantitative comparison of backbone architecture on BUSI dataset. \(\uparrow\) denotes the higher the better and \(\downarrow\) denotes the lower the better. Red indicates the best results and blue represents the second-best results. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**LPF** & **HPF (Without Denoising)** & **HPF** & **mDice (\%)** & **mIoU (\%)** \\ \hline ✓ & & & 81.07 & 72.34 \\ ✓ & ✓ & & 80.31 (-0.76) & 71.49 (-0.85) \\ ✓ & & ✓ & 81.83 (+0.76) & 73.50 (+1.16) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Quantitative comparison of variants of NSM on BUSI dataset. Red values enclosed in parentheses refer to improvement compared with our model with only low-pass filter within NSM, while the blue ones indicates reductions. Figure 7: Visualization results of the ablative experiment on BUSI [19] (first row and second row) and Dataset B [21] (third row and fourth row). The red curve is the ground truth boundary. The green curve is the segmentation results of different components. ultrasound imaging is increasingly widely used in clinical pre-screening and is becoming the mainstream trend. However, the segmentation of breast tumors suffers from the inherent limitations of ultrasound images, including the presence of speckle noise and the issue of indistinct boundaries in malignant tumors. Speckle noise is inevitable in ultrasound images, causing strong interference during neural network training, thereby reducing the model's generalization ability. Simultaneously, the blurred boundaries of malignant tumors also lead to decreased model accuracy, which is detrimental to intelligent diagnosis. To address these issues, we discussed how to effectively suppress speckle noise from a frequency perspective and designed a coarse-to-fine paradigm, namely NSBR-Net, which shows outstanding segmentation performance and brings new insights into ultrasound image analysis. The proposed breast tumor segmentation model exhibited superior accuracy over competing algorithms, achieving mDice, mIoU, and MAE scores of 81.83%, 73.50%, and 3.55% on the BUSI dataset and 81.48%, 73.08%, and 1.74% on Dataset B, respectively. Compared to the state-of-the-art transformer-based method, there was a significant improvement of 3.67% on Dataset B and 2.30% on BUSI in mDice, in the testing of malignant tumors, which holds great significance for the clinical diagnosis of cancer. Moreover, as can be seen in Figure 6, NSBR-Net showed no issues of false positives, unlike other segmentation models, which are obviously affected by speckle noise. We attribute this capability to our NSM module, which filters out noise information from coarse-grained feature mappings while preserving detailed boundary information. Considering the significant individual differences in breast tumors (shown in Figure 6), one of our future research directions will focus on developing appropriate data augmentation algorithms to expand the sample space and enhance the generalization capabilities of our model further. Since our model is designed for two-dimensional ultrasound images, another future direction is to extend the methodology to three-dimensional images. Furthermore, considering the requirement for real-time performance in clinical diagnostic assistance, enhancing the computational efficiency of the model is also a crucial direction for future research. Therefore, we plan to conduct in-depth evaluations and optimizations of the model's computational performance in our future studies.