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This study introduces a subject-specific spatial-angular Gaussian field for self-supervised joint k-q diffusion MRI (dMRI) reconstruction, addressing the limitations of existing methods that fail to leverage the shared anatomical organization of diffusion-weighted images. By utilizing overlapping 3D Gaussian primitives that respond to q-conditioned tensor-residuals, the method synthesizes signals from undersampled k-space measurements, effectively coupling spatial regions and diffusion directions. Experiments on HCP diffusion shells reveal significant enhancements in the reconstruction of missing-direction dMRI data and improvements in tensor-derived metrics and principal diffusion orientation estimation.
Joint k-q dMRI reconstruction can be dramatically improved by leveraging shared anatomical information and local signal variations through a novel Gaussian field approach.
Diffusion MRI requires repeated k-space acquisitions over multiple diffusion-encoding directions, making acquisition time dependent on both spatial and angular sampling. Existing joint k-q methods either associate directional parameters with fixed voxels or separate spatial reconstruction from angular completion. However, diffusion-weighted images acquired under different directions share the same anatomical organization, while their local signal intensities vary with diffusion encoding. Existing formulations do not fully exploit the complementarity between shared anatomy and direction-dependent signal variation. Consequently, residual spatial errors may be misinterpreted as genuine angular variation and propagated to unobserved directions. We propose a subject-specific spatial-angular Gaussian field for self-supervised joint k-q dMRI reconstruction. Shared 3D Gaussian primitives provide local spatial support, with each primitive carrying a continuous q-conditioned tensor-residual response. The signal at each location is synthesized from multiple overlapping primitive responses, coupling neighboring spatial regions and diffusion directions. The field is progressively optimized from undersampled k-space measurements of observed directions, without fully sampled targets or held-out-direction supervision. Experiments on three HCP diffusion shells under multiple acceleration settings demonstrated consistent improvements in missing-direction DWI reconstruction, tensor-derived metrics, and principal diffusion orientation estimation.
