MR-FusionMamba: A Visual Mamba Network with Range-Null Decomposition for Multi-Modal MRI reconstruction

Accelerated multi-modal magnetic resonance imaging (MRI) offers an effective solution for fast MRI, excelling in reconstructing the target modality from its under-sampled counterpart with the assistance of a reference modality. Current deep learning methods for accelerated MRI primarily utilize convolutional neural networks (CNNs) or Transformers to extract features and integrate various types of data. While CNNs are efficient, their limited receptive fields constrain their ability to capture global context. Meanwhile, Transformers excel at modeling global information but are challenged by their quadratic computational complexity. Recent advancements in the State Space Model (SSM), particularly Mamba, offer a promising solution to this issue by enabling global awareness with linear complexity. Thus, we propose MR-FusionMamba to perform efficient multi-modal MRI reconstruction, which integrates Mamba blocks into dual U-shaped networks and extends their functionality to support dual inputs. To improve the data-consistency, we apply the Range-Null Decomposition theorem to our network. We evaluate our method with extensive experiments on the BraTS dataset, demonstrating that our method achieves state-of-the-art (SOTA) performance.