beta-FFT: Nonlinear Interpolation and Differentiated Training Strategies for Semi-Supervised Medical Image Segmentation

Co-Training has achieved significant success in the field of semi-supervised learning(SSL); however, the homogenization phenomenon, which arises from multiple models tending towards similar decision boundaries, remains inadequately addressed. To tackle this issue, we propose a novel algorithm called β-FFT from the perspectives of data processing and training structure. In data processing, we apply diverse augmentations to input data and feed them into two sub-networks. To balance the training instability caused by different augmentations during consistency learning, we introduce a nonlinear interpolation technique based on the Fast Fourier Transform (FFT). By swapping low-frequency components between variously augmented images, this method not only generates smooth and diverse training samples that bridge different augmentations but also enhances the model’s generalization capability while maintaining consistency learning stability. In training structure, we devise a differentiated training strategy to mitigate homogenization in co-training. Specifically, we use labeled data for additional training of one model within the co-training framework, while for unlabeled data, we employ linear interpolation based on the Beta(β) distribution as a regularization technique in additional training. This approach allows for more efficient utilization of limited labeled data and simultaneously improves the model’s performance on unlabeled data, optimizing overall system performance. Code is available at the following link. https://github.com/Xi-Mu-Yu/beta-FFT.