Year: 2017
Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 1 : pp. 1–21
Abstract
We propose a reliable direct imaging method based on the reverse time migration for finding extended obstacles with phaseless total field data. We prove that the imaging resolution of the method is esseentially the same as the imaging results using the scattering data with full phase information when the measurement is far away from the obstacle. The imaginary part of the cross-correlation imaging functional always peaks on the boundary of the obstacle. Numerical experiments are included to illustrate the powerful imaging quality.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2017.m1617
Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 1 : pp. 1–21
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
-
Some recent developments in the unique determinations in phaseless inverse acoustic scattering theory
Zhang, Deyue | Guo, YukunElectronic Research Archive, Vol. 29 (2021), Iss. 2 P.2149
https://doi.org/10.3934/era.2020110 [Citations: 4] -
Inverse elastic scattering problems with phaseless far field data
Ji, Xia | Liu, XiaodongInverse Problems, Vol. 35 (2019), Iss. 11 P.114004
https://doi.org/10.1088/1361-6420/ab2a35 [Citations: 19] -
Uniqueness in Inverse Scattering Problems with Phaseless Far-Field Data at a Fixed Frequency
Xu, Xiaoxu | Zhang, Bo | Zhang, HaiwenSIAM Journal on Applied Mathematics, Vol. 78 (2018), Iss. 3 P.1737
https://doi.org/10.1137/17M1149699 [Citations: 29] -
An Approximate Factorization Method for Inverse Acoustic Scattering with Phaseless Total-Field Data
Zhang, Bo | Zhang, HaiwenSIAM Journal on Applied Mathematics, Vol. 80 (2020), Iss. 5 P.2271
https://doi.org/10.1137/19M1280612 [Citations: 1] -
Recovery of an infinite rough surface by a nonlinear integral equation method from phaseless near-field data
Li, Lili | Li, JianliangJournal of Inverse and Ill-posed Problems, Vol. 0 (2022), Iss. 0
https://doi.org/10.1515/jiip-2021-0045 [Citations: 0] -
Single‐slice microwave imaging of breast cancer by reverse time migration
Bilgin, Egemen | Çayören, Mehmet | Joof, Sulayman | Cansiz, Gökhan | Yilmaz, Tuba | Akduman, IbrahimMedical Physics, Vol. 49 (2022), Iss. 10 P.6599
https://doi.org/10.1002/mp.15917 [Citations: 3] -
Recovering Unbounded Rough Surfaces with a Direct Imaging Method
Zhang, Hai-wen
Acta Mathematicae Applicatae Sinica, English Series, Vol. 36 (2020), Iss. 1 P.119
https://doi.org/10.1007/s10255-020-0916-5 [Citations: 2] -
A direct imaging method for the half-space inverse scattering problem with phaseless data
Chen, Zhiming | Fang, Shaofeng | Huang, GuanghuiInverse Problems & Imaging, Vol. 11 (2017), Iss. 5 P.901
https://doi.org/10.3934/ipi.2017042 [Citations: 10] -
Inverse Acoustic Scattering with Phaseless Far Field Data: Uniqueness, Phase Retrieval, and Direct Sampling Methods
Ji, Xia | Liu, Xiaodong | Zhang, BoSIAM Journal on Imaging Sciences, Vol. 12 (2019), Iss. 2 P.1163
https://doi.org/10.1137/18M1236022 [Citations: 18] -
Uniqueness results on phaseless inverse acoustic scattering with a reference ball
Zhang, Deyue | Guo, YukunInverse Problems, Vol. 34 (2018), Iss. 8 P.085002
https://doi.org/10.1088/1361-6420/aac53c [Citations: 34] -
In-Wall Imaging for the Reconstruction of Obstacles by Reverse Time Migration
Yarar, M. Lütfi | Yapar, AliSensors, Vol. 23 (2023), Iss. 9 P.4456
https://doi.org/10.3390/s23094456 [Citations: 1] -
Imaging of buried obstacles in a two-layered medium with phaseless far-field data
Li, Long | Yang, Jiansheng | Zhang, Bo | Zhang, HaiwenInverse Problems, Vol. 37 (2021), Iss. 5 P.055004
https://doi.org/10.1088/1361-6420/abec1d [Citations: 5] -
A neural network scheme for recovering scattering obstacles with limited phaseless far-field data
Yin, Weishi | Yang, Wenhong | Liu, HongyuJournal of Computational Physics, Vol. 417 (2020), Iss. P.109594
https://doi.org/10.1016/j.jcp.2020.109594 [Citations: 54] -
Uniqueness in Inverse Scattering Problems with Phaseless Far-Field Data at a Fixed Frequency. II
Xu, Xiaoxu | Zhang, Bo | Zhang, HaiwenSIAM Journal on Applied Mathematics, Vol. 78 (2018), Iss. 6 P.3024
https://doi.org/10.1137/18M1196820 [Citations: 22] -
Direct Imaging Methods for Reconstructing a Locally Rough Interface from Phaseless Total-Field Data or Phased Far-Field Data
Li, Long | Yang, Jiansheng | Zhang, Bo | Zhang, HaiwenSIAM Journal on Imaging Sciences, Vol. 17 (2024), Iss. 1 P.188
https://doi.org/10.1137/23M1571393 [Citations: 1] -
Recovering scattering obstacles by multi-frequency phaseless far-field data
Zhang, Bo | Zhang, HaiwenJournal of Computational Physics, Vol. 345 (2017), Iss. P.58
https://doi.org/10.1016/j.jcp.2017.05.022 [Citations: 45] -
Simultaneous recovery of an obstacle and its excitation sources from near-field scattering data
Chang, Yan | Guo, YukunElectronic Research Archive, Vol. 30 (2022), Iss. 4 P.1296
https://doi.org/10.3934/era.2022068 [Citations: 5] -
Target Reconstruction with a Reference Point Scatterer using Phaseless Far Field Patterns
Ji, Xia | Liu, Xiaodong | Zhang, BoSIAM Journal on Imaging Sciences, Vol. 12 (2019), Iss. 1 P.372
https://doi.org/10.1137/18M1205789 [Citations: 22] -
Uniqueness in phaseless inverse scattering problems with known superposition of incident point sources
Sun, Fenglin | Zhang, Deyue | Guo, YukunInverse Problems, Vol. 35 (2019), Iss. 10 P.105007
https://doi.org/10.1088/1361-6420/ab3373 [Citations: 10] -
Phaseless inverse source scattering problem: Phase retrieval, uniqueness and direct sampling methods
Ji, Xia | Liu, Xiaodong | Zhang, BoJournal of Computational Physics: X, Vol. 1 (2019), Iss. P.100003
https://doi.org/10.1016/j.jcpx.2019.100003 [Citations: 10] -
A direct imaging method for the exterior and interior inverse scattering problems
Zhang, Deyue | Wu, Yue | Wang, Yinglin | Guo, YukunInverse Problems and Imaging, Vol. 16 (2022), Iss. 5 P.1299
https://doi.org/10.3934/ipi.2022025 [Citations: 6] -
Uniqueness in inverse electromagnetic scattering problem with phaseless far-field data at a fixed frequency
Xu, Xiaoxu | Zhang, Bo | Zhang, HaiwenIMA Journal of Applied Mathematics, Vol. (2020), Iss.
https://doi.org/10.1093/imamat/hxaa024 [Citations: 4] -
Reverse time migration for inverse obstacle scattering with a generalized impedance boundary condition
Li, Jianliang
Applicable Analysis, Vol. 101 (2022), Iss. 1 P.48
https://doi.org/10.1080/00036811.2020.1727894 [Citations: 1] -
Periodic surface identification with phase or phaseless near-field data
Zheng, Jinchang | Cheng, Jin | Li, Peijun | Lu, ShuaiInverse Problems, Vol. 33 (2017), Iss. 11 P.115004
https://doi.org/10.1088/1361-6420/aa8cb3 [Citations: 6] -
Near-field imaging of inhomogeneities in a stratified ocean waveguide
Liu, Keji
Journal of Computational Physics, Vol. 398 (2019), Iss. P.108901
https://doi.org/10.1016/j.jcp.2019.108901 [Citations: 7] -
Fast imaging of scattering obstacles from phaseless far-field measurements at a fixed frequency
Zhang, Bo | Zhang, HaiwenInverse Problems, Vol. 34 (2018), Iss. 10 P.104005
https://doi.org/10.1088/1361-6420/aad81f [Citations: 20] -
A fast preconditioned iterative method for the electromagnetic scattering by multiple cavities with high wave numbers
Zhao, Meiling | Zhu, NaJournal of Computational Physics, Vol. 398 (2019), Iss. P.108826
https://doi.org/10.1016/j.jcp.2019.07.025 [Citations: 11] -
Uniqueness and Direct Imaging Method for Inverse Scattering by Locally Rough Surfaces with Phaseless Near-Field Data
Xu, Xiaoxu | Zhang, Bo | Zhang, HaiwenSIAM Journal on Imaging Sciences, Vol. 12 (2019), Iss. 1 P.119
https://doi.org/10.1137/18M1210204 [Citations: 8] -
Uniqueness in inverse cavity scattering problems with phaseless near-field data
Zhang, Deyue | Wang, Yinglin | Guo, Yukun | Li, JingzhiInverse Problems, Vol. 36 (2020), Iss. 2 P.025004
https://doi.org/10.1088/1361-6420/ab53ee [Citations: 13] -
Exact Multistatic Interferometric Imaging via Generalized Wirtinger Flow
Yonel, Bariscan | Son, Il-Young | Yazici, BirsenIEEE Transactions on Computational Imaging, Vol. 6 (2020), Iss. P.711
https://doi.org/10.1109/TCI.2020.2967151 [Citations: 15] -
Imaging small polarizable scatterers with polarization data
Bardsley, Patrick | Cassier, Maxence | Guevara Vasquez, FernandoInverse Problems, Vol. 34 (2018), Iss. 10 P.104002
https://doi.org/10.1088/1361-6420/aad342 [Citations: 3] -
Reconstructions of a Rough Surface Based on a Nonlinear Integral Equation Method from Phaseless Near-Field Data
李, 莉莉
Advances in Applied Mathematics, Vol. 11 (2022), Iss. 01 P.359
https://doi.org/10.12677/AAM.2022.111044 [Citations: 0]