Equivariant Bootstrapping for Uncertainty Quantification in Imaging Inverse Problems
Equivariant Bootstrapping for Uncertainty Quantification in Imaging Inverse Problems
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DOI：
10.48550/arxiv.2310.11838
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发表时间：
2023-10
期刊：
影响因子：
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通讯作者：
Julian Tachella;Marcelo Pereyra
中科院分区：
文献类型：
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作者：
Julian Tachella;Marcelo Pereyra
科学成像问题通常是严重不适定的，因此具有显著的内在不确定性。因此，准确地量化这些问题的解决方案中的不确定性是至关重要的实验结果的严格解释，以及可靠地使用重建图像作为科学证据。不幸的是，现有的成像方法是无法量化的不确定性，在重建图像的方式是强大的实验重复。本文提出了一种新的不确定性量化方法的基础上，利用对称性和成像问题中常见的不变性的参数自举算法的等变配方。此外，所提出的方法是通用的，可以很容易地应用于任何图像重建技术，包括无监督的训练策略，可以单独从观察到的数据进行训练，从而使不确定性量化的情况下，没有地面实况数据可用。我们通过一系列数值实验并通过与最先进的替代不确定性量化策略（例如涉及基于分数的扩散模型和Langevin采样器的贝叶斯策略）的比较来演示所提出的方法。在我们所有的实验中，所提出的方法提供了非常准确的高维置信区域，并在估计精度，不确定性量化精度和计算时间方面优于竞争方法。
Scientific imaging problems are often severely ill-posed, and hence have significant intrinsic uncertainty. Accurately quantifying the uncertainty in the solutions to such problems is therefore critical for the rigorous interpretation of experimental results as well as for reliably using the reconstructed images as scientific evidence. Unfortunately, existing imaging methods are unable to quantify the uncertainty in the reconstructed images in a manner that is robust to experiment replications. This paper presents a new uncertainty quantification methodology based on an equivariant formulation of the parametric bootstrap algorithm that leverages symmetries and invariance properties commonly encountered in imaging problems. Additionally, the proposed methodology is general and can be easily applied with any image reconstruction technique, including unsupervised training strategies that can be trained from observed data alone, thus enabling uncertainty quantification in situations where there is no ground truth data available. We demonstrate the proposed approach with a series of numerical experiments and through comparisons with alternative uncertainty quantification strategies from the state-of-the-art, such as Bayesian strategies involving score-based diffusion models and Langevin samplers. In all our experiments, the proposed method delivers remarkably accurate high-dimensional confidence regions and outperforms the competing approaches in terms of estimation accuracy, uncertainty quantification accuracy, and computing time.