Sparse Subspace Diffusion Model for Physically Consistent Accelerated MRI Reconstruction

Abstract

Magnetic resonance imaging (MRI) provides excellent soft-tissue contrast but suffers from long acquisition times. Accelerated MRI alleviates this issue by undersampling k-space, but this approach introduces aliasing artifacts and information loss. Traditional compressed sensing methods exploit handcrafted sparse priors, whereas deep learning approaches learn data-driven priors, but both often struggle at high acceleration rates due to severe information degradation. This study introduces a diffusion-based reconstruction framework, termed the Sparse Subspace Diffusion Model (SSDM), that performs MRI reconstruction within an adaptive sparse space. The proposed approach integrates coupling convolutional dictionary learning with diffusion-based generative modeling to decompose MR images into multiple orthogonal sparse subspaces and reconstruct them under measurement-consistency constraints. This formulation enables diffusion modeling in a physically meaningful latent space, effectively bridging the gap between data-driven learning and physics-guided reconstruction. Experimental results on the fastMRI dataset demonstrate that the proposed method achieves higher reconstruction quality than existing diffusion- and sparsity-based approaches, with better preservation of fine details and suppression of artifacts across various acceleration factors.