High-Order State Space Model for Multi-Modal Accelerated MRI Reconstruction

In this work, we propose a novel high-order state space model embedded within an interpretable unfolding algorithm for MRI reconstruction, marking the first adaptation of the Mamba framework to this domain. Traditional methods often rely on stacking second-order interactions through transformer architectures to capture high-order global information. However, these approaches exhibit inherent quadratic complexity, resulting in significant computational overhead and limiting their efficiency in practical environments. Through a reexamination of the intrinsic properties of Mamba, we observe that it is fundamentally a first-order function and leveraging this insight, we introduce a high-order variant of Mamba, wherein the linear complexity attention mechanism within the initial Mamba is shared across successive Mamba calculations, achieving the same functionality while mitigating the computational cost of stacked methods. This adaptation allows our model to retain the benefits of cascaded modeling while significantly improving computational efficiency. By capturing high-order interactions more efficiently, our approach strikes a balance between performance and resource usage, providing a practical solution for accelerated MRI reconstruction. Furthermore, extensive experiments on multiple MRI benchmark datasets demonstrate that our approach delivers competitive performance compared to other state-of-the-arts.