论文标题
分解方法的正则化，并应用于逆散射
Regularization of the Factorization Method with Applications to Inverse Scattering
论文作者
论文摘要
在这里，我们讨论了在希尔伯特空间上作用的积极操作员的定期化方法。分解方法是一种定性重建方法，用于解决许多逆形状问题。通常，定性方法试图使用几乎没有先验信息来重建未知对象的形状。这里提出的正则化分解方法旨在避免反转算法中的数值不稳定性。这允许人们以计算简单且在分析上严格的方式恢复未知的结构。我们将讨论正则分解方法与来自声学反向散射的示例的理论和应用。还将使用合成数据显示数值示例以显示该方法的适用性。
Here we discuss a regularized version of the factorization method for positive operators acting on a Hilbert Space. The factorization method is a qualitative reconstruction method that has been used to solve many inverse shape problems. In general, qualitative methods seek to reconstruct the shape of an unknown object using little to no a priori information. The regularized factorization method presented here seeks to avoid numerical instabilities in the inversion algorithm. This allows one to recover unknown structures in a computationally simple and analytically rigorous way. We will discuss the theory and application of the regularized factorization method to examples coming from acoustic inverse scattering. Numerical examples will also be presented using synthetic data to show the applicability of the method.
