论文标题
质量 - 巴约西亚方法与部分数据相反的声源问题
Quality-Bayesian approach to inverse acoustic source problems with partial data
论文作者
论文摘要
提出了一种质量的bayesian方法，结合了直接采样方法和贝叶斯反转，提议使用部分数据重建未知声源的位置和强度。首先，我们通过构造新的指标函数来扩展直接采样方法以获得源的近似位置。分析指标的行为。其次，使用贝叶斯公式将逆问题提出为统计推断问题。证明了后验分布的适当性。在第一步中获得的源位置是在先验中编码的。然后，使用MECMC算法来探索后密度。这两个步骤都使用相同的物理模型和测量数据。数值实验表明，即使有部分数据，该提出的方法也有效。
A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling method by constructing a new indicator function to obtain the approximate locations of the sources. The behavior of the indicator is analyzed. Second, the inverse problem is formulated as a statistical inference problem using the Bayes' formula. The well-posedness of the posterior distribution is proved. The source locations obtained in the first step are coded in the priors. Then an Metropolis-Hastings MCMC algorithm is used to explore the posterior density. Both steps use the same physical model and measured data. Numerical experiments show that the proposed method is effective even with partial data.
