用扩散模型先验解决反问题中的观测参数估计与不确定性量化
Estimation of instrument and noise parameters for inverse problem based on prior diffusion model
- 基于扩散模型先验构建贝叶斯框架下的参数估计方法
- 可同时优化观测参数与待恢复图像，且计算高效
- 支持后验采样与不确定性量化，适合高精度反问题场景
本文研究反问题中观测参数（响应与误差参数）的估计问题。重点考虑在贝叶斯框架下引入正则化且先验由扩散过程建模的情形。此时后验采样存在困难，但近期工作提出一种简洁有效的解决方案，并展现出显著灵活性，可用于观测参数估计。所提策略可定义观测参数与待恢复图像的最优估计量，同时提供不确定性量化手段。结合MCMC算法可计算估计值及后验性质，并具备一定理论保障。文中多个数值实验验证了该方法在计算效率和估计质量方面的优越性。
原文摘要 · Abstract (English)
This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a diffusion process. In this context, the issue of posterior sampling is known to be thorny, and a recent paper proposes a notably simple and effective solution. Additionally, it opens an remarkable flexibility when it comes to estimating observation parameters. The proposed strategy enables to define an optimal estimator for both observation parameters and image of interest. Furthermore, the strategy provides a means for uncertainty quantification. In addition, MCMC algorithms allow for the computation of estimates and properties of posteriors, while offering some guarantees. The paper presents several numerical experiments that clearly confirm the computational efficiency and the quality of both estimates and uncertainty quantification.
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