用线性采样法识别受限傅里叶积分算子的形状和参数

IF 2 2区数学 Q1 MATHEMATICS, APPLIED

Inverse Problems Pub Date : 2024-07-25 DOI:10.1088/1361-6420/ad5e18

Lorenzo Audibert and Shixu Meng

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引用次数: 0

摘要

本文提供了一种基于相同数据但数据算子定义不同的新线性采样方法，适用于两个反问题：固定观测方向的多频反源问题和博恩反散射问题。我们证明，当正则化参数趋近于零时，相关的正则化线性采样指标会收敛到小邻域中未知数的平均值。我们建立了形状识别理论和参数识别理论，并借助原球面波函数及其广义来激发、分析和实现这两个理论。我们进一步提出了一种基于原形的线性采样方法，并通过数值实验证明了这种线性采样方法如何能够重建形状和参数。

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Shape and parameter identification by the linear sampling method for a restricted Fourier integral operator

In this paper we provide a new linear sampling method based on the same data but a different definition of the data operator for two inverse problems: the multi-frequency inverse source problem for a fixed observation direction and the Born inverse scattering problems. We show that the associated regularized linear sampling indicator converges to the average of the unknown in a small neighborhood as the regularization parameter approaches to zero. We develop both a shape identification theory and a parameter identification theory which are stimulated, analyzed, and implemented with the help of the prolate spheroidal wave functions and their generalizations. We further propose a prolate-based implementation of the linear sampling method and provide numerical experiments to demonstrate how this linear sampling method is capable of reconstructing both the shape and the parameter.

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来源期刊

Inverse Problems 数学-物理：数学物理

CiteScore

4.40

自引率

14.30%

发文量

115

审稿时长

2.3 months

期刊介绍： An interdisciplinary journal combining mathematical and experimental papers on inverse problems with theoretical, numerical and practical approaches to their solution. As well as applied mathematicians, physical scientists and engineers, the readership includes those working in geophysics, radar, optics, biology, acoustics, communication theory, signal processing and imaging, among others. The emphasis is on publishing original contributions to methods of solving mathematical, physical and applied problems. To be publishable in this journal, papers must meet the highest standards of scientific quality, contain significant and original new science and should present substantial advancement in the field. Due to the broad scope of the journal, we require that authors provide sufficient introductory material to appeal to the wide readership and that articles which are not explicitly applied include a discussion of possible applications.