Empirical Bayesian Imaging With Large-Scale Push-Forward Generative Priors
Empirical Bayesian Imaging With Large-Scale Push-Forward Generative Priors
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DOI：
10.1109/lsp.2024.3361806
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发表时间：
2024
影响因子：
3.9
通讯作者：
Savvas Melidonis;M. Holden;Y. Altmann;Marcelo Pereyra;K. Zygalakis
中科院分区：
文献类型：
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作者：
Savvas Melidonis;M. Holden;Y. Altmann;Marcelo Pereyra;K. Zygalakis
我们提出了一种利用深度生成先验进行成像反问题贝叶斯推理的新方法。现代贝叶斯成像通常依赖于基于分数的扩散生成先验，它提供了显著的点估计，但明显低估了不确定性。诸如变分自编码器和生成对抗网络之类的前推模型提供了一个健壮的替代方案，导致贝叶斯模型被证明是适定的，并且对小问题产生准确的不确定性量化结果。然而，由于偏差、模态崩溃和多模态等问题，前推模型在大问题上的适用范围较差。我们建议通过在经验贝叶斯框架内嵌入条件深度生成先验来解决这一困难。我们使用超分辨率架构考虑生成先验，并使用贝叶斯计算策略进行推理，该策略同时计算感兴趣的低分辨率图像的最大边际似然估计（MMLE），并有条件地从高分辨率图像的后验分布中提取蒙特卡罗样本到观测数据和MMLE。该方法通过图像去模糊实验和与最先进的比较来证明。
We propose a new methodology for leveraging deep generative priors for Bayesian inference in imaging inverse problems. Modern Bayesian imaging often relies on score-based diffusion generative priors, which deliver remarkable point estimates but significantly underestimate uncertainty. Push-forward models such as variational auto-encoders and generative adversarial networks provide a robust alternative, leading to Bayesian models that are provably well-posed and which produce accurate uncertainty quantification results for small problems. However, push-forward models scale poorly to large problems because of issues related to bias, mode collapse and multimodality. We propose to address this difficulty by embedding a conditional deep generative prior within an empirical Bayesian framework. We consider generative priors with a super-resolution architecture, and perform inference by using a Bayesian computation strategy that simultaneously computes the maximum marginal likelihood estimate (MMLE) of the low-resolution image of interest, and draws Monte Carlo samples from the posterior distribution of the high-resolution image, conditionally to the observed data and the MMLE. The methodology is demonstrated with an image deblurring experiment and comparisons with the state-of-the-art.