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首页> 外文期刊>Journal of Computational Physics >A variational Bayesian method to inverse problems with impulsive noise
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A variational Bayesian method to inverse problems with impulsive noise

机译：脉冲噪声逆问题的变分贝叶斯方法

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摘要

We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise to achieve robustness with respect to outliers. A hierarchical model with all hyper-parameters automatically determined from the given data is described. An algorithm of variational type by minimizing the Kullback-Leibler divergence between the true posteriori distribution and a separable approximation is developed. The numerical method is illustrated on several one- and two-dimensional linear and nonlinear inverse problems arising from heat conduction, including estimating boundary temperature, heat flux and heat transfer coefficient. The results show its robustness to outliers and the fast and steady convergence of the algorithm.
机译：我们提出了一种新颖的数值方法，用于解决可能受到大量离群值影响的脉冲噪声引起的逆问题。该方法是贝叶斯类型的，它利用重尾t分布来处理数据噪声，以实现针对异常值的鲁棒性。描述了具有根据给定数据自动确定的所有超参数的分层模型。通过最小化真实后验分布和可分离逼近之间的Kullback-Leibler散度，开发了一种变分类型算法。针对由热传导引起的几个一维和二维线性和非线性逆问题，举例说明了数值方法，包括估计边界温度，热通量和传热系数。结果表明，该算法具有较强的鲁棒性和快速稳定的收敛能力。

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