论文标题
在反问题中不确定性定量的分数得分匹配
Denoising Score-Matching for Uncertainty Quantification in Inverse Problems
论文作者
论文摘要
事实证明，深层神经网络在解决广泛的反问题方面非常有效，但大多数情况下，它们提供的解决方案的不确定性很难量化。在这项工作中，我们提出了一个通用的贝叶斯框架，可以解决逆问题，在该问题中，我们限制了对信号上先前分布的深神经网络的使用。我们采用最近的DeNoisingsCore匹配技术来从数据中学习这一点，并随后使用退火的Hamiltonian Monte-Carlo方案的Aspart来品尝整个图像逆问题。我们将此框架应用于磁共振图（MRI）重建，并说明该方法不仅如何产生高质量重建，而且还可以用于评估重建图像的特定特定表现的不确定性。
Deep neural networks have proven extremely efficient at solving a wide rangeof inverse problems, but most often the uncertainty on the solution they provideis hard to quantify. In this work, we propose a generic Bayesian framework forsolving inverse problems, in which we limit the use of deep neural networks tolearning a prior distribution on the signals to recover. We adopt recent denoisingscore matching techniques to learn this prior from data, and subsequently use it aspart of an annealed Hamiltonian Monte-Carlo scheme to sample the full posteriorof image inverse problems. We apply this framework to Magnetic ResonanceImage (MRI) reconstruction and illustrate how this approach not only yields highquality reconstructions but can also be used to assess the uncertainty on particularfeatures of a reconstructed image.
