KMD: Koopman Multi-modality Decomposition for Generalized Brain Tumor Segmentation under Incomplete Modalities

Magnetic resonance imaging (MRI), with modalities including T1, T2, T1ce, and Flair, providing complementary information critical for sub-region analysis, is widely used for brain tumor diagnosis. However, clinical practice often suffers from varying degrees of incompleteness of necessary modalities due to reasons such as susceptibility to artifacts. It significantly impairs segmentation model performance. Given the limited available modalities at hand, existing approaches attempt to project them into a shared latent space. However, they ignore decomposing the modality-shared and modality-specific information and failed to construct the relationship among different modalities. Such deficiency limits the effectiveness of the segmentation performance, particularly at a time when the amount of data in each modality is different. In this paper, we propose the plug-and-play Koopman Multi-modality Decomposition (KMD) module, leveraging the Koopman Invariant Subspace to disentangle modality-common and modality-specific information. It is capable of constructing modality relationships that minimize bias toward modalities across various modality-incomplete scenarios. More importantly, it can be integrated into several existing backbones feasibility. Through theoretical deductions and extensive empirical experiences on the BraTS2018 and BraTS2020 datasets, we have sufficiently demonstrated the effectiveness of the proposed KMD to promote generalization performance.