Sub-DM: Subspace Diffusion Model With Orthogonal Decomposition for MRI Reconstruction

Diffusion model-based approaches recently achieved remarkable success in MRI reconstruction, but in tegration into clinical routine remains challenging due to its time-consuming convergence. This phenomenon is particularly notable when directly apply conventional diffusion process to k-space data without considering the inherent properties of k-space sampling, limiting k-space learning efficiency and image reconstruction quality. To tackle these challenges, we introduce subspace diffusion model with or thogonal decomposition, a method (referred to as Sub-DM) that restrict the diffusion process via projections onto sub space as the k-space data distribution evolves toward noise. Particularly, the orthogonal decomposition strategy constructs a low-rank subspace using stacked wavelet tensor. This enables the diffusion process to generate accurate priors with fewer iterations and enhances model generalization by focusing on low-dimensional intrinsic features. Owing to its near-reversible property, the strategy preserves information integrity while facilitating bidirectional refinement of model across different spaces, thereby enriching prior knowledge from diverse dimensions. Comprehensive experiments on different datasets clearly demonstrate that Sub-DM achieves faster convergence speed and exhibits more robust generalization ability.