提出一种无需训练的后处理方法,让加速MRI重建结果更符合实际扫描数据。
Measured-Subspace Consistency: A Plug-and-Play Operator for Diffusion Posterior Sampling in Accelerated MRI Reconstruction

- 在图像空间对采样结果做一致性修正,强制满足已测量的k空间数据
- 使样本间差异集中在不可观测的空域,已测区域差异降低16.5倍以上
- 适用于各类扩散采样器,无需重训练,适合临床部署
加速MRI的扩散后验采样器虽能准确重建,但不同样本间在已测量的k空间上仍存在分歧,导致不确定性被错误放大。本文将此现象归因于‘已测子空间泄漏’,即违反了物理可实现性。为此提出互补的已测与未测子空间分散度度量(MSD/USD),并设计测量子空间一致性(MSC)——一种无需训练的终端修正机制,可封装任意兼容的图像空间后验采样器,采用标准多线圈一致性锁。理论上证明理想变换可将样本间差异限制在MRI零空间内,并量化了实际灵敏度加权实现中的残余跨子空间耦合。在六种基础采样器及两类人体解剖结构上验证,包括膝关节先验用于脑部重建的分布外转移场景,MSC显著降低软采样器的已测子空间分散度(如五种脑部对比度下DPS中位数降低16.5倍,最高达29倍),同时保持未测子空间多样性,对一致型采样器近乎无影响。此外,MSC维持或轻微提升PSNR/SSIM,无需重新训练、调参或引入显著计算开销。
原文摘要 · Abstract (English)
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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