Unique determinations in inverse scattering problems with phaseless near-field measurements

Deyue Zhang; Yukun Guo; Fenglin Sun; Hongyu Liu

doi:10.3934/ipi.2020026

Article Contents

2020, Volume 14, Issue 3: 569-582. Doi: 10.3934/ipi.2020026

This issue Previous Article Robust reconstruction of fluorescence molecular tomography with an optimized illumination pattern Next Article

Unique determinations in inverse scattering problems with phaseless near-field measurements

1.
School of Mathematics, Jilin University, Changchun 130012, China
2.
School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
3.
Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong SAR, China

^* Corresponding authors: Yukun Guo and Hongyu Liu
^* Corresponding authors: Yukun Guo and Hongyu Liu

Received: November 2019

Published: March 2020

The first and third authors are supported by NSFC grant 11671170. The second author is supported by NSFC grants 11971133, 11601107, 11671111 and 41474102. The fourth author is supported by Hong Kong RGC General Research Funds, 12302017, 12301218, 12302919

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Abstract

In this paper, we establish the unique determination results for several inverse acoustic scattering problems using the modulus of the near-field data. By utilizing the superpositions of point sources as the incident waves, we rigorously prove that the phaseless near-fields collected on an admissible surface can uniquely determine the location and shape of the obstacle as well as its boundary condition and the refractive index of a medium inclusion, respectively. We also establish the uniqueness in determining a locally rough surface from the phaseless near-field data due to superpositions of point sources. These are novel uniqueness results in inverse scattering with phaseless near-field data.

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Mathematics Subject Classification: Primary: 78A46, 74J25; Secondary: 45Q05, 35R30, 31B20.

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Figure 1. An illustration of the phaseless inverse scattering by a bounded scatterer

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Figure 2. An illustration of the phaseless inverse scattering by a locally perturbed half-plane

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