带背景信息的相位检索和无相位反向散射

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Thorsten Hohage, Roman G Novikov, Vladimir N Sivkin
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引用次数: 0

摘要

我们考虑的问题是,在固定能量下,如何从微分散射截面(散射振幅的平方模)中找到多维薛定谔方程中的紧凑支撑势。在玻恩近似中,这一问题简化为相位检索问题,即根据球上傅里叶变换的绝对值重建势。为了弥补缺失的相位信息,我们采用了先验已知背景散射体的方法。特别是,我们提出了一种迭代方案,通过测量单个微分散射截面来寻找电势,该截面对应于未知电势与已知背景电势之和,且两者之间有足够的不连续性。如果放宽这一条件,那么我们也能给出类似的结果,即通过对未知电势的差分散射截面进行额外的单色测量,在不考虑背景电势的情况下找到电势。我们通过数值示例演示了所提算法的性能。在本研究中,我们大大推进了阿加尔佐夫等人(2019 逆问题 35 24001)以及诺维科夫和西夫金(2021 逆问题 37 055011)的理论和数值研究。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Phase retrieval and phaseless inverse scattering with background information
We consider the problem of finding a compactly supported potential in the multidimensional Schrödinger equation from its differential scattering cross section (squared modulus of the scattering amplitude) at fixed energy. In the Born approximation this problem simplifies to the phase retrieval problem of reconstructing the potential from the absolute value of its Fourier transform on a ball. To compensate for the missing phase information we use the method of a priori known background scatterers. In particular, we propose an iterative scheme for finding the potential from measurements of a single differential scattering cross section corresponding to the sum of the unknown potential and a known background potential, which is sufficiently disjoint. If this condition is relaxed, then we give similar results for finding the potential from additional monochromatic measurements of the differential scattering cross section of the unknown potential without the background potential. The performance of the proposed algorithms is demonstrated in numerical examples. In the present work we significantly advance theoretically and numerically studies of Agaltsov et al (2019 Inverse Problems 35 24001) and Novikov and Sivkin (2021 Inverse Problems 37 055011).
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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