New MSC operator cuts MRI reconstruction dispersion by up to 29x

Accelerated MRI reconstruction using diffusion posterior samplers can produce accurate images, but they suffer from a critical flaw: different samples often disagree on the k-space coefficients that the scanner has already measured. This 'measured-subspace leakage' violates the physical measurement constraint and inflates uncertainty. To quantify it, the authors introduce new metrics (MSD/USD). Their solution, Measured-Subspace Consistency (MSC), is a plug-and-play operator that wraps any compatible image-space posterior sampler with a multi-coil consistency lock. The ideal lock follows classical range/null-space data consistency, repurposed here as a black-box posterior audit and correction rather than a new reconstructor.

In experiments across six base samplers and two MRI anatomies (including out-of-distribution transfer from knee to brain), MSC dramatically reduces measured-subspace dispersion—a median 16.5x reduction for DPS across five brain contrasts, up to ~29x—while leaving unmeasured-subspace diversity intact. It also maintains or modestly improves PSNR/SSIM without retraining, retuning, or significant computational overhead. The theoretical proof ensures pairwise sample differences are confined to the MRI null space. This work offers a practical, zero-fuss fix for diffusion-based MRI reconstruction pipelines.