论文标题
贝叶斯反演的非平稳多层高斯先生
Non-Stationary Multi-layered Gaussian Priors for Bayesian Inversion
论文作者
论文摘要
在本文中，我们研究了多层高斯先验的贝叶斯逆问题。我们首先根据随机部分微分方程系统来描述有条件的高斯层。我们使用有限维盖尔金方法构建计算推理方法。我们表明，所提出的近似具有与原始多层模型解决方案的收敛性概率属性。然后，我们使用预处理的曲柄 - Nicolson算法进行贝叶斯推断，该算法经过修改以与多层高斯田地合作。我们通过信号反卷积和计算机化X射线断层扫描问题的数值实验显示，该方法可以同时提供平滑和边缘保存。
In this article, we study Bayesian inverse problems with multi-layered Gaussian priors. We first describe the conditionally Gaussian layers in terms of a system of stochastic partial differential equations. We build the computational inference method using a finite-dimensional Galerkin method. We show that the proposed approximation has a convergence-in-probability property to the solution of the original multi-layered model. We then carry out Bayesian inference using the preconditioned Crank--Nicolson algorithm which is modified to work with multi-layered Gaussian fields. We show via numerical experiments in signal deconvolution and computerized X-ray tomography problems that the proposed method can offer both smoothing and edge preservation at the same time.
