Measured-Subspace Consistency: A Plug-and-Play Operator for Diffusion Posterior Sampling in Accelerated MRI Reconstruction

• URL: http://arxiv.org/abs/2606.28448v1
• Date: Fri, 26 Jun 2026 08:49:39 GMT
• Title: Measured-Subspace Consistency: A Plug-and-Play Operator for Diffusion Posterior Sampling in Accelerated MRI Reconstruction
• Abstract summary: Diffusion posterior samplers for accelerated MRI can reconstruct accurately yet still disagree on the acquired k-space across samples.<n>We identify this measured-subspace leakage as a physical-admissibility failure.<n>We 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.
• Score: 2.4827516038838064
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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