ABSTRACT

In this paper, we consider a cavity reconstruction problem for the interior acoustic scattering from limited-aperture measurements. To recover the shape of the cavity, the Bayesian inference technique is applied with the information of posterior distribution of the unknown object being explored in terms of the measured data. The posterior distribution provides us with sufficient knowledge about the unknowns, and therefore it can be used to give the corresponding estimation. We discuss the well-posedness of the posterior distribution in the sense of the Hellinger metric and use the preconditioned Crank–Nicolson (pCN) sampling technique to generate the posterior samples. Numerical examples show the effectiveness of the proposed algorithm.

摘要

在本文中，我们考虑了有限孔径测量的内部声学散射的腔重建问题。为了恢复空腔的形状，贝叶斯推理技术被应用于根据测量数据探索的未知物体的后验分布信息。后验分布为我们提供了关于未知数的足够知识，因此它可以用来给出相应的估计。我们在 Hellinger 度量的意义上讨论后验分布的适定性，并使用预处理的 Crank-Nicolson (pCN) 采样技术来生成后验样本。数值例子表明了所提出算法的有效性。