LMO: Linear Mamba Operator for MRI Reconstruction

Interpretability and consistency have long been crucial factors in MRI reconstruction. While interpretability has been significantly innovated with the emerging deep unfolding networks, current solutions still suffer from inconsistency issues and produce inferior anatomical structures. Especially in out-of-distribution cases, e.g., when the acceleration rate (AR) varies, the generalization performance is often catastrophic. To counteract the dilemma, we propose an innovative Linear Mamba Operator (LMO) to ensure consistency and generalization, while still enjoying desirable interpretability. Theoretically, we argue that mapping between function spaces, rather than between signal instances, provides a solid foundation of high generalization. Technically, LMO achieves a good balance between global integration facilitated by a state space model that scans the whole function domain, and local integration engaged with an appealing property of continuous-discrete equivalence. On that basis, learning holistic features can be guaranteed, tapping the potential of maximizing data consistency. Quantitative and qualitative results demonstrate that LMO significantly outperforms other state-of-the-arts. More importantly, LMO is the unique model that, with AR changed, achieves retraining performance without retraining steps. Codes are attached and will be released on GitHub.