HSMD: A Hilbert-scanning mamba dense network for 3D MRI reconstruction

Long MRI acquisition times motivate the use of k-space undersampling for accelerated imaging, but undersampling often introduces aliasing artifacts and structural detail loss. Existing 2D slice-wise reconstruction methods fail to fully exploit inter-slice anatomical correlations. This study develops a Hilbert-Scanning Mamba Dense Network (HSMD) for high-quality 3D MRI reconstruction, which leverages inter-slice contextual information to improve reconstruction fidelity. The proposed HSMD consists of a Shallow Feature Extraction Module (SFEM) and five cascaded Multi-Directional Spatial Attention (MDSA) modules. The SFEM is responsible for extracting local detailed features and coarse-scale structural context from undersampled MRI inputs. The MDSA modules extract and fuse multi-directional spatial information along the depth, height, and width dimensions to enhance the representation of 3D structural features. Furthermore, a multi-directional Hilbert selective state-space scanning strategy is introduced into MDSA to capture long-range spatial dependencies within 3D volumetric data, thereby improving structural representation while preserving spatial locality. Experimental results on the BraTS and UCSF-PDGM datasets under diverse acceleration factors validate that the proposed HSMD achieves superior performance over state-of-the-art methods in both quantitative metrics and visual quality. The HSMD exhibits excellent capability in 3D undersampled MRI reconstruction, holding promising prospects for efficient and reliable clinical MRI applications.