ProtoWave-Mamba: A Semi-Supervised Approach for Ocean Internal Wave Segmentation with Wavelet Enhancement and Long-Range Sequence Modeling

Ocean internal wave segmentation from remote sensing imagery is a challenging task due to the elongated morphology of targets, blurred boundaries, and the high cost of pixel-level annotations. To address these issues, this paper proposes ProtoWave-Mamba (PWM-Net), an end-to-end semi-supervised segmentation framework specifically tailored to the physical characteristics of ocean internal waves. Specifically, it synergistically integrates multi-scale wavelet transforms to enhance weak texture information in the frequency domain, a Mamba architecture with linear-complexity long-range modeling to capture global contextual dependencies of slender structures, and a class prototype alignment module to extract category-wise feature centers from a very limited set of labeled samples. By enforcing cross-sample alignment in the feature space, the proposed method guides the distribution of unlabeled data and performs prototype-guided pseudo-label denoising to suppress the noise accumulation inherent in pseudo-label-based semi-supervised learning. Consequently, ProtoWave-Mamba achieves efficient semi-supervised knowledge transfer and significantly improves boundary representation and feature discrimination with only 30 labeled images per dataset. Experimental results on two representative ocean internal wave datasets demonstrate that the proposed method consistently outperforms state-of-the-art semi-supervised methods. In particular, compared with the best-performing baseline Mean Teacher, it achieves substantial improvements in Intersection over Union (IoU), Dice coefficient, and Recall, especially under complex background conditions. Ablation studies further confirm the effectiveness of each core module in maintaining contour continuity and fine-grained segmentation quality.