论文标题
使用多个频率限制的光圈数据的反声源问题的确定性统计方法
Deterministic-Statistical Approach for an Inverse Acoustic Source Problem using Multiple Frequency Limited Aperture Data
论文作者
论文摘要
我们建议使用多个频率限制的光圈远处数据为逆源问题提出了一种确定性统计方法。直接采样方法用于获得圆盘，以便它包含源的紧凑支持。光盘的Dirichlet本征函数用于扩展源函数。然后，逆问题是重铸，作为扩展系数的统计推断问题，贝叶斯反转用于重建系数。统计逆问题相对于测得的数据的稳定性在Hellinger距离的意义上是合理的。实施了预处理的曲柄 - 尼科尔森（PCN）大都市束缚（MH）算法，以探索未知数的后验密度函数。数值示例表明，在有限的句子数据下，所提出的方法对于平滑和非平滑源都是有效的。
We propose a deterministic-statistical method for an inverse source problem using multiple frequency limited aperture far field data. The direct sampling method is used to obtain a disc such that it contains the compact support of the source. The Dirichlet eigenfunctions of the disc are used to expand the source function. Then the inverse problem is recast as a statistical inference problem for the expansion coefficients and the Bayesian inversion is employed to reconstruct the coefficients. The stability of the statistical inverse problem with respect to the measured data is justified in the sense of Hellinger distance. A preconditioned Crank-Nicolson (pCN) Metropolis-Hastings (MH) algorithm is implemented to explore the posterior density function of the unknowns. Numerical examples show that the proposed method is effective for both smooth and non-smooth sources given limited-aperture data.
