论文标题
一种直接抽样方法，用于同时恢复不同性质的不均匀夹杂物
A Direct Sampling Method for Simultaneously Recovering Inhomogeneous Inclusions of Different Nature
论文作者
论文摘要
在这项工作中，我们研究了仅在一个或两个测量事件下收集的非常有限的边界Cauchy数据，旨在同时恢复由两个不同物理参数引起的多个不均匀的包含物。我们为同时重建过程提出了一种新的快速，稳定和高度可行的直接采样方法（DSM）。构建了两组探测和索引功能，并分析其所需的属性。为了识别和解除不同物理性质的多个不均匀的包含，我们引入了一个新的几乎正交性属性的新概念，该概念概述了经典DSMS中几乎正交性属性的重要概念，用于同一物理性质的非均匀夹杂物。在这个新概念的帮助下，我们制定了一种可靠的策略，以区分两种不同类型的不均匀夹杂物，并在一个或两个测量事件下收集嘈杂的数据。我们通过选择适当的边界涌入来进一步提高解耦效果。提出了数值实验，以说明所提出方法的鲁棒性和效率。
In this work, we investigate a class of elliptic inverse problems and aim to simultaneously recover multiple inhomogeneous inclusions arising from two different physical parameters, using very limited boundary Cauchy data collected only at one or two measurement events. We propose a new fast, stable and highly parallelable direct sampling method (DSM) for the simultaneous reconstruction process. Two groups of probing and index functions are constructed, and their desired properties are analyzed. In order to identify and decouple the multiple inhomogeneous inclusions of different physical nature, we introduce a new concept of mutually almost orthogonality property that generalizes the important concept of almost orthogonality property in classical DSMs for inhomogeneous inclusions of same physical nature. With the help of this new concept, we develop a reliable strategy to distinguish two different types of inhomogeneous inclusions with noisy data collected at one or two measurement events. We further improve the decoupling effect by choosing an appropriate boundary influx. Numerical experiments are presented to illustrate the robustness and efficiency of the proposed method.
