用得分函数统一多种数据驱动先验，提升贝叶斯逆问题采样效率。
Bridging data-driven priors via the score function for posterior sampling -- Comparative review and experimental study
- 通过得分函数统一四种数据驱动先验，构建通用框架。
- 在图像修复与超分辨率任务中表现优异，真实地质图像恢复也有效。
- 适合研究贝叶斯反演、生成模型融合的科研人员参考。
本文回顾了贝叶斯逆问题中常用的多种数据驱动先验，发现它们可通过各自的得分函数实现统一建模。基于这一共同视角，这些先验可无缝集成到一种新型采样算法中，显著提升采样效率。实验验证了正则化去噪、基于归一化流的先验、基于得分的生成模型及凸岭正则化四类先验在图像修补和单图超分辨率任务中的性能。此外，在地质场景采集的真实图像恢复中也取得良好效果。该统一框架具备普适性，适用于由广泛得分函数定义的后验分布，超越本文所考察的具体案例。
原文摘要 · Abstract (English)
This paper reviews how a diverse set of popular data-driven priors commonly used in Bayesian inverse problems can be unified through their respective score functions. By framing these priors under this common perspective, we show that they can benefit from their straightfoward and effective integration into a recently proposed sampling algorithm. The applicability of this common framework is illustrated by considering several data-driven priors, namely regularization-by-denoising, normalizing flow-based priors, score-based generative models, and convex-ridge regularizers. For these four particular priors, the performance of the method is evaluated when conducting image inpainting and single image super-resolution. These results, as well as those obtained when restoring real images acquired in a geological context, demonstrate the efficiency of the method. This unified framework proves versatile enough to handle any posterior distribution defined by a broad class of score function-based priors, beyond the specific cases considered in this paper.
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