Multi-modal MRI offers valuable complementary information for diagnosis and treatment; however, its utility is limited by prolonged scanning times. To accelerate the acquisition process, a practical approach is to reconstruct images of the target modality, which requires longer scanning times, from under-sampled k-space data using the fully-sampled reference modality with shorter scanning times as guidance. The primary challenge of this task is comprehensively and efficiently integrating complementary information from different modalities to achieve high-quality reconstruction. Existing methods struggle with this: 1) convolution-based models fail to capture long-range dependencies; 2) transformer-based models, while excelling in global feature modeling, struggle with quadratic computational complexity. To address this, we propose MMR-Mamba, a novel framework that thoroughly and efficiently integrates multi-modal features for MRI reconstruction, leveraging Mamba's capability to capture long-range dependencies with linear computational complexity while exploiting global properties of the Fourier domain. Specifically, we first design a Target modality-guided Cross Mamba (TCM) module in the spatial domain, which maximally restores the target modality information by selectively incorporating relevant information from the reference modality. Then, we introduce a Selective Frequency Fusion (SFF) module to efficiently integrate global information in the Fourier domain and recover high-frequency signals for the reconstruction of structural details. Furthermore, we devise an Adaptive Spatial-Frequency Fusion (ASFF) module, which mutually enhances the spatial and frequency domains by supplementing less informative channels from one domain with corresponding channels from the other.
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