发表机构
Johns Hopkins University; University of California, Los Angeles（约翰斯·霍普金斯大学; 加利福尼亚大学洛杉矶分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对贝叶斯成像逆问题采样成本高的痛点，提出基于近端朗之万动力学与Picard迭代的并行采样框架PiX-MC，实现50倍加速且保持重建质量
AI 中文摘要
贝叶斯成像逆问题通常需要从高维后验分布中采样。尽管近期的基于得分的模型和扩散模型提供了表达力强的贝叶斯先验，但它们的采样过程本质上仍是串行的，对于大规模成像应用而言计算成本高昂。我们提出PiX-MC，一种基于近端朗之万动力学和Picard迭代的时间并行后验采样框架。近端似然公式利用了许多成像似然能接受高效、特定问题的近端算子这一事实，而Picard细化则在离散化节点间暴露了并行性，天然支持多GPU实现。为进一步提升实际可扩展性和采样性能，我们开发了该框架的多块变体和退火变体。我们在透明假设下建立了收敛保证，可容纳非对数凹后验、不完善的学习得分模型、多块实现以及退火调度。对多种成像逆问题的实验表明，PiX-MC在保持重建质量的同时大幅缩短了挂钟时间。在512×512×80的稀疏视图计算机断层扫描（CT）问题上，退火多块PiX-MC使用8个GPU实现了比标准朗之万采样器高达50倍的运行时加速。
英文摘要
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.
