Approximate Lipschitz stability for phaseless inverse scattering with background information

IF 0.9 4区数学 Q2 MATHEMATICS

Journal of Inverse and Ill-Posed Problems Pub Date : 2023-05-03 DOI:10.1515/jiip-2023-0001

V. Sivkin

引用次数: 3

Abstract

Abstract We prove approximate Lipschitz stability for monochromatic phaseless inverse scattering with background information in dimension d ≥ 2 {d\geq 2} . Moreover, these stability estimates are given in terms of non-overdetermined and incomplete data. Related results for reconstruction from phaseless Fourier transforms are also given. Prototypes of these estimates for the phased case were given in [R. G. Novikov, Approximate Lipschitz stability for non-overdetermined inverse scattering at fixed energy, J. Inverse Ill-Posed Probl. 21 2013, 6, 813–823].

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具有背景信息的无相逆散射的近似Lipschitz稳定性

摘要本文证明了具有d≥2维背景信息的单色无相逆散射近似Lipschitz稳定性{\geq 2}。此外，这些稳定性估计是根据非超定和不完全数据给出的。本文还给出了无相傅里叶变换重建的相关结果。在[R]中给出了分阶段情况下这些估计的原型。李建军，李建军，李建军，等。非定能逆散射的近似Lipschitz稳定性[j].计算机工程学报，2013,36(6):813-823。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Inverse and Ill-Posed Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.60

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： This journal aims to present original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published. Issues of the Journal of Inverse and Ill-Posed Problems contain high quality papers which have an innovative approach and topical interest. The following topics are covered: Inverse problems existence and uniqueness theorems stability estimates optimization and identification problems numerical methods Ill-posed problems regularization theory operator equations integral geometry Applications inverse problems in geophysics, electrodynamics and acoustics inverse problems in ecology inverse and ill-posed problems in medicine mathematical problems of tomography