Measured-Subspace Consistency: A Plug-and-Play Operator for Diffusion Posterior Sampling in Accelerated MRI Reconstruction
For MRI reconstruction practitioners, this provides a simple, plug-and-play fix to ensure physical admissibility in diffusion posterior sampling without retraining.
The paper identifies measured-subspace leakage in diffusion posterior samplers for accelerated MRI, where posterior variability disagrees with acquired k-space data. It proposes Measured-Subspace Consistency (MSC), a training-free operator that enforces data consistency, reducing measured-subspace dispersion by up to ~29x while preserving unmeasured diversity and maintaining or improving PSNR/SSIM.
Diffusion posterior samplers for accelerated MRI can reconstruct accurately yet still disagree on the acquired k-space across samples, placing posterior variability on coefficients the scanner has already measured. We identify this measured-subspace leakage as a physical-admissibility failure. Under a hard-constraint model it violates the measurement constraint and inflates the reported uncertainty with disagreement about coefficients the scanner has already determined. To quantify this leakage, we introduce complementary measured- and unmeasured-subspace k-space dispersion metrics (MSD/USD). We then present Measured-Subspace Consistency (MSC), a training-free terminal correction that wraps any compatible image-space posterior sampler with a standard multi-coil consistency lock. The ideal lock follows classical range/null-space data consistency. Our contribution is to repurpose it as a black-box posterior audit and correction rather than a new reconstructor or learned sampler. Theoretically, we prove that the ideal transform confines pairwise sample differences to the MRI null space and bound the residual cross-subspace coupling left by practical sensitivity-weighted implementations. Across six base samplers and two MRI anatomies, including out-of-distribution transfer where a knee prior reconstructs brain, MSC substantially reduces measured-subspace dispersion for Soft samplers (a median 16.5x reduction for DPS across five brain contrasts, up to ~29x), while preserving unmeasured-subspace diversity and acting as a near-identity map for Consistent ones. Furthermore, MSC maintains or modestly improves PSNR/SSIM, with no retraining, retuning, or significant computational overhead.