Accurate segmentation of carotid arteries in ultrasound imaging is critical for stroke risk assessment. However, speckle noise, low contrast, and blurred boundaries remain major challenges. In this paper, we propose a Frequency-Spatial Synergy Network (FSS-Net) to achieve noise-robust and high-precision carotid artery segmentation. The network integrates wavelet transform, multi-domain attention, and edge enhancement into a unified encoder-decoder architecture. Specifically, a Channel-Spatial-Wavelet Attention (CSWA) module is designed to suppress noise and purify semantic features in the frequency domain. A Wavelet-Enhanced Bottleneck (WEB) module is introduced to capture long-range global dependencies efficiently. Furthermore, a Laplacian-Guided Adaptive Edge Fusion (LAEF) module compensates high-frequency details and maintains boundary continuity. Extensive experiments on carotid ultrasound datasets show that FSS-Net achieves a Dice score (DSC) of 96.46% and strong robustness under low SNR conditions, outperforming several state-of-the-art methods. This method realizes accurate segmentation of carotid artery in ultrasonic imaging, effectively identifies carotid atherosclerotic plaque, and is verified by other task (such as segmentation of breast cancer), suggesting that it has good clinical application potential in identifying abnormal tissue masses in ultrasonic images.