UNIQUE DETERMINATIONS IN INVERSE SCATTERING PROBLEMS WITH PHASELESS NEAR-FIELD MEASUREMENTS

Deyue ZHANG; Yukun GUO; Fenglin SUN; Hongyu LIU

doi:10.3934/ipi.2020026

UNIQUE DETERMINATIONS IN INVERSE SCATTERING PROBLEMS WITH PHASELESS NEAR-FIELD MEASUREMENTS

Deyue ZHANG
, Yukun GUO^*
, Fenglin SUN
, Hongyu LIU^*

^*Corresponding author for this work

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

21 Citations (Scopus)

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.

Original language	English
Pages (from-to)	569-582
Journal	Inverse Problems and Imaging
Volume	14
Issue number	3
Online published	Mar 2020
DOIs	https://doi.org/10.3934/ipi.2020026
Publication status	Published - Jun 2020

Research Keywords

Uniqueness
phaseless
inverse scattering
near field
point source
acoustic wave

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10.3934/ipi.2020026

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title = "UNIQUE DETERMINATIONS IN INVERSE SCATTERING PROBLEMS WITH PHASELESS NEAR-FIELD MEASUREMENTS",

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.",

keywords = "Uniqueness, phaseless, inverse scattering, near field, point source, acoustic wave",

author = "Deyue ZHANG and Yukun GUO and Fenglin SUN and Hongyu LIU",

year = "2020",

month = jun,

doi = "10.3934/ipi.2020026",

language = "English",

volume = "14",

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AU - ZHANG, Deyue

AU - GUO, Yukun

AU - SUN, Fenglin

AU - LIU, Hongyu

PY - 2020/6

Y1 - 2020/6

N2 - 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.

AB - 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.

KW - Uniqueness

KW - phaseless

KW - inverse scattering

KW - near field

KW - point source

KW - acoustic wave

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U2 - 10.3934/ipi.2020026

DO - 10.3934/ipi.2020026

M3 - RGC 21 - Publication in refereed journal

SN - 1930-8337

VL - 14

SP - 569

EP - 582

JO - Inverse Problems and Imaging

JF - Inverse Problems and Imaging

IS - 3

ER -

UNIQUE DETERMINATIONS IN INVERSE SCATTERING PROBLEMS WITH PHASELESS NEAR-FIELD MEASUREMENTS

Abstract

Research Keywords

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GRF: Mathematical and Computational Studies of Geomagnetic Anomaly Detections

GRF: Mathematical Analysis on Scattering from Corner Singularities, Inverse Shape Problems and Geometric Structures of Transmission Eigenfunctions

GRF: Some Theoretical and Numerical Studies for Inverse Problems in Wave Propagations

Cite this

UNIQUE DETERMINATIONS IN INVERSE SCATTERING PROBLEMS WITH PHASELESS NEAR-FIELD MEASUREMENTS

Abstract

Research Keywords

Access Output

Other Access Options

Permanent Link

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Projects

GRF: Mathematical and Computational Studies of Geomagnetic Anomaly Detections

GRF: Mathematical Analysis on Scattering from Corner Singularities, Inverse Shape Problems and Geometric Structures of Transmission Eigenfunctions

GRF: Some Theoretical and Numerical Studies for Inverse Problems in Wave Propagations

Cite this