Picard Proximal Monte Carlo for Parallel Bayesian Imaging with Score-Based Generative Priors

2026-08-18

AI Summary

该研究针对贝叶斯成像逆问题中高维后验分布采样效率低的问题，提出了一种基于近端朗之万动力学和Picard迭代的并行采样框架PiX-MC。

Abstract

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.

Problem

• Bayesian Imaging
• Score-Based Generative Priors
• Posterior Sampling
• Parallel Computing
• Langevin Dynamics

Innovation

• proximal Langevin dynamics
• Picard iteration
• parallel posterior sampling
• multi-GPU implementation
• annealed variants