Inverse scattering via nonlinear integral equations method for a sound-soft crack with phaseless data.

DOI10.21136/AM.2018.0154-17zbMath1488.35621OpenAlexW2796318198WikidataQ129989818 ScholiaQ129989818MaRDI QIDQ1642874

Heping Dong, Peng Gao, Fuming Ma

Publication date: 15 June 2018

Published in: Applications of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.21136/am.2018.0154-17

zbMATH Keywords

Helmholtz equationcracktranslation invariancephaselessinverse scattering problem

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for inverse problems for integral equations (65R32) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46)

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Cites Work

• Identification of sound-soft 3D obstacles from phaseless data
• Shape reconstructions from phaseless data
• The method of fundamental solutions for the identification of a sound-soft obstacle in inverse acoustic scattering
• On integral equations of the first kind with logarithmic kernels
• Unique determination of a sound-soft ball by the modulus of a single far field datum
• Shape reconstruction of acoustic obstacles from the modulus of the far field pattern
• Nonlinear integral equation methods for the reconstruction of an acoustically sound-soft obstacle
• Phased and Phaseless Domain Reconstructions in the Inverse Scattering Problem via Scattering Coefficients
• Shape reconstruction of the multi-scale rough surface from multi-frequency phaseless data
• Inverse scattering for planar cracks via nonlinear integral equations
• Inverse scattering from an open arc
• On the inverse acoustic scattering problem by an open arc: the sound-hard case
• A hybrid method for two-dimensional crack reconstruction
• Fréchet differentiability of the far field operator for scattering from a crack
• A linear sampling method for inverse scattering from an open arc
• Reconstruction of an acoustically sound-soft obstacle from one incident field and the far-field pattern
• Inverse acoustic and electromagnetic scattering theory
• Unnamed Item