Newton s method for inverse obstacle scattering meets the method of least squares

DOI10.1088/0266-5611/19/6/056zbMath1052.65055OpenAlexW2094148293MaRDI QIDQ4466429

Publication date: 10 June 2004

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0266-5611/19/6/056

zbMATH Keywords

numerical example integral equation Newton's method regularization Helmholtz equation nonlinear ill-posed problems inverse obstacle scattering inverse scattering problems

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Nonlinear ill-posed problems (47J06) Numerical solutions to equations with nonlinear operators (65J15) Numerical methods for ill-posed problems for integral equations (65R30) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46)

Related Items

A novel study on the MUSIC-type imaging of small electromagnetic inhomogeneities in the limited-aperture inverse scattering problem, Iterative methods for planar crack reconstruction in semi-infinite domains, Looking Back on Inverse Scattering Theory, An iterative scheme for imaging acoustic obstacle from phaseless total-field data, Numerical solution of an inverse obstacle scattering problem with near-field data, The method of fundamental solutions for the identification of a scatterer with impedance boundary condition in interior inverse acoustic scattering, Huygens' principle and iterative methods in inverse obstacle scattering, A hybrid method for sound-hard obstacle reconstruction, Uniqueness and reconstruction method for inverse elastic wave scattering with phaseless data, A neural network warm-start approach for the inverse acoustic obstacle scattering problem, Inverse Obstacle Scattering for Elastic Waves with Phased or Phaseless Far-Field Data, On the solution of direct and inverse multiple scattering problems for mixed sound-soft, sound-hard and penetrable objects, Direct sampling method for identifying magnetic inhomogeneities in limited-aperture inverse scattering problem, A second degree Newton method for an inverse obstacle scattering problem, Improvement of direct sampling method in transverse electric polarization, A combination of shape and conductivity function reconstruction methods for an inverse boundary value problem, A reference ball based iterative algorithm for imaging acoustic obstacle from phaseless far-field data, A Bayesian level set method for an inverse medium scattering problem in acoustics, Inverse obstacle scattering for acoustic waves in the time domain, A hybrid method for inverse boundary value problems for an inclusion in semi-infinite two-dimensional domains, Near-field imaging of obstacles, Iterative methods for planar crack reconstruction in semi-infinite domains, Inverse Scattering, Localization of small obstacles from back-scattered data at limited incident angles with full-waveform inversion, A second order Newton method for sound soft inverse obstacle scattering, An inverse acoustic-elastic interaction problem with phased or phaseless far-field data, A numerical study of single source localization algorithms for phaseless inverse scattering problems, A shape calculus analysis for tracking type formulations in electrical impedance tomography, An iterative decomposition method for scatterer reconstruction in \(\mathbb{R}^3\)