Incomplete Multi-modal Brain Tumor Segmentation via Learnable Sorting State Space Model

Brain tumor segmentation plays a crucial role in clinical diagnosis, yet the frequent unavailability of certain MRI modalities poses a significant challenge. In this paper, we introduce the Learnable Sorting State Space Model (LS3M), a novel framework designed to maximize the utilization of available modalities for brain tumor segmentation. LS3M excels at efficiently modeling long-range dependencies based on the Mamba design, while incorporating differentiable permutation matrices that reorder input sequences based on modality-specific characteristics. This dynamic reordering ensures that critical spatial inductive biases and long-range semantic correlations inherent in 3D brain MRI are preserved, which is crucial for imcomplete multi-modal brain tumor segmentation.Once the input sequences are reordered using the generated permutation matrix, the Series State Space Model (S3M) block models the relationships between them, capturing both local and long-range dependencies. This enables effective representation of intra-modal and inter-modal relationships, significantly improving segmentation accuracy.Additionally, LS3M incorporates a global input strategy, augmented with relative position embeddings, providing richer contextual information and notably enhancing spatial awareness. Extensive experiments on the BraTS2018 and BraTS2020 datasets demonstrate that LS3M outperforms existing methods, offering a robust solution for brain tumor segmentation, particularly in scenarios with missing modalities.