提出并行贝叶斯成像采样方法,大幅加速图像重建。
Picard Proximal Monte Carlo for Parallel Bayesian Imaging with Score-Based Generative Priors

- 基于邻近朗之万动力学与皮卡德迭代,实现时间并行采样。
- 在512×512×80的稀疏视角CT任务中,提速达50倍。
- 适合大规模图像重建,支持多GPU高效部署。
贝叶斯成像反问题常需从高维后验分布中采样。尽管近期基于分数的扩散模型提供了强大的先验,但其采样过程仍为串行且计算昂贵。本文提出PiX-MC,一种基于邻近朗之万动力学与皮卡德迭代的并行后验采样框架。邻近似然形式利用了成像似然函数可高效计算特定问题的邻近算子,而皮卡德精炼则暴露离散节点间的并行性,天然支持多GPU实现。为进一步提升可扩展性与采样性能,我们设计了多块和退火变体。在透明假设下建立了收敛性保证,可处理非对数凹后验、不完美学习得分模型、多块实现及退火调度。在多种成像反问题上实验表明,PiX-MC显著减少运行时间同时保持重建质量。在512×512×80稀疏视角计算机断层扫描(CT)任务中,退火多块PiX-MC在八张GPU上相较标准朗之万采样器实现最高50倍的运行时加速。
原文摘要 · Abstract (English)
Bayesian imaging inverse problems often require sampling from high-dimensional posterior distributions. While recent score-based and diffusion models provide expressive Bayesian priors, their sampling procedures remain inherently sequential and computationally expensive for large-scale imaging applications. We propose PiX-MC, a time-parallel posterior sampling framework based on proximal Langevin dynamics and Picard iteration. The proximal-likelihood formulation exploits the fact that many imaging likelihoods admit efficient, problem-specific proximal operators, while Picard refinement exposes parallelism across discretization nodes and naturally supports multi-GPU implementation. To further improve practical scalability and sampling performance, we develop multi-block and annealed variants of the proposed framework. We establish convergence guarantees under transparent assumptions, accommodating non-log-concave posteriors, imperfect learned score models, multi-block implementations, and annealing schedules. Experiments on a diverse collection of imaging inverse problems demonstrate that PiX-MC substantially reduces wall-clock time while preserving reconstruction quality. On a $512\times512\times80$ sparse-view computed tomography (CT) problem, annealed multi-block PiX-MC achieves up to a $50\times$ runtime speedup over the standard Langevin sampler using eight GPUs.
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