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

2026-06-26

AI Summary

This work addresses the issue of measurement subspace leakage in diffusion posterior sampling for accelerated MRI reconstruction, which causes inconsistency among samples in the observed k-space coefficients, violating physical plausibility and artificially inflating uncertainty. To resolve this, the authors propose Measurement Subspace Correction (MSC), a training-free end-to-end correction method that integrates any image-space posterior sampler with multi-coil consistency constraints, enforcing sample discrepancies to reside solely within the MRI null space and thereby guaranteeing consistency in the measured subspace. The approach innovatively reformulates classical data consistency as a black-box posterior auditing and correction mechanism, with theoretical guarantees on controlling subspace coupling. Experiments demonstrate that MSC reduces measurement subspace dispersion by a median factor of 16.5 across six samplers and two anatomies, preserves diversity in the unmeasured subspace, maintains or slightly improves PSNR/SSIM, and incurs no additional training or computational overhead.

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.

Problem

• measured-subspace leakage
• diffusion posterior sampling
• accelerated MRI reconstruction
• physical-admissibility failure
• k-space consistency

Innovation

• Measured-Subspace Consistency
• Diffusion Posterior Sampling
• Accelerated MRI Reconstruction
• Data Consistency
• Plug-and-Play Operator