Sparse Subspace Diffusion Model for Physically Consistent Accelerated MRI Reconstruction

Xiangyao Deng, Zhiqiang Shen, Sanuwani Dayarathna, Juan P. Meneses, Sergio Uribe, Zhaolin Chen

Keywords: Magnetic resonance imaging (MRI); fastMRI, Diffusion model; Convolutional dictionary learning; Physics-informed learning

Abstract:

Magnetic resonance imaging (MRI) offers excellent soft-tissue contrast but is limited by long acquisition times. Accelerated MRI alleviates this issue by undersampling k-space, which, however, introduces aliasing artifacts and information loss. Traditional compressed sensing methods exploit handcrafted sparse priors, whereas deep learning approaches learn data-driven priors but often struggle at high acceleration rates due to severe information degradation.
This study introduces a unified diffusion-based reconstruction framework that performs MRI reconstruction within an adaptive sparse space. The proposed approach integrates convolutional dictionary learning and 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 improved reconstruction quality compared to existing diffusion- and sparsity-based approaches, exhibiting better fine-detail preservation and artifact suppression across various acceleration factors.

Primary Subject Area: Image Acquisition and Reconstruction

Secondary Subject Area: Generative Models

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Originality Policy: Yes

Single-blind & Not Under Review Elsewhere: Yes

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Submission Number: 200