Identification of small inhomogeneities: Asymptotic factorization

DOI10.1090/S0025-5718-07-01946-1zbMath1119.35111MaRDI QIDQ3433762

Roland Griesmaier, Martin Hanke, Habib Ammari

Publication date: 2 May 2007

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

zbMATH Keywords

asymptotic expansionsintegral equation methodselectrical impedance tomographyreconstruction algorithmsfactorization methodssmall conductivity inhomogeneities

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Inverse problems for PDEs (35R30) Asymptotic expansions of solutions to PDEs (35C20)

Related Items (16)

Enhanced multilevel linear sampling methods for inverse scattering problems ⋮ The imaging of small perturbations in an anisotropic media ⋮ Electrostatic backscattering by insulating obstacles ⋮ A note on the MUSIC algorithm for impedance tomography ⋮ A multifrequency MUSIC algorithm for locating small inhomogeneities in inverse scattering ⋮ An Approximate Factorization Method for Inverse Acoustic Scattering with Phaseless Total-Field Data ⋮ Asymptotic expansion for harmonic functions in the half‐space with a pressurized cavity ⋮ Expansion Methods ⋮ Mathematical Framework for Abdominal Electrical Impedance Tomography to Assess Fatness ⋮ Sampling Methods ⋮ Reconstruction of Small Inclusions in Electrical Impedance Tomography Problems ⋮ OPTIMAL EDGE DETECTION BY TOPOLOGICAL ASYMPTOTIC ANALYSIS ⋮ High Precision Identification of an Object: Optimality-Conditions-Based Concept of Imaging ⋮ On the Justification of the Foldy--Lax Approximation for the Acoustic Scattering by Small Rigid Bodies of Arbitrary Shapes ⋮ Analysis of the Acoustic Waves Reflected by a Cluster of Small Holes in the Time-Domain and the Equivalent Mass Density ⋮ Reconstructing acoustic obstacles by planar and cylindrical waves

Cites Work

• Unnamed Item
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• Electromagnetic scattering by small dielectric inhomogeneities.
• Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter. II: The full Maxwell equations.
• Identification of small inhomogeneities of extreme conductivity by boundary measurements: A theorem on continuous dependence
• A direct impedance tomography algorithm for locating small inhomogeneities
• Boundary layer techniques for solving the Helmholtz equation in the presence of small inhomogeneities
• Reconstruction of small inhomogeneities from boundary measurements
• The factorization method for real elliptic problems
• Explicit Characterization of Inclusions in Electrical Impedance Tomography
• The MUSIC-algorithm and the factorization method in inverse scattering theory for inhomogeneous media
• A sampling method for detecting buried objects using electromagnetic scattering
• Finite Element Methods for Navier-Stokes Equations
• Boundary Integral Operators on Lipschitz Domains: Elementary Results
• Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction
• Characterization of the shape of a scattering obstacle using the spectral data of the far field operator
• Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume
• A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction
• Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements
• Recovery of Small Inhomogeneities from the Scattering Amplitude at a Fixed Frequency
• High-Order Terms in the Asymptotic Expansions of the Steady-State Voltage Potentials in the Presence of Conductivity Inhomogeneities of Small Diameter
• Recent progress in electrical impedance tomography
• Recent Developments in Inverse Acoustic Scattering Theory
• A Regularized Sampling Method for Solving Three-Dimensional Inverse Scattering Problems
• Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter
• The factorization method for a class of inverse elliptic problems
• A simple method for solving inverse scattering problems in the resonance region
• The Linear Sampling Method for Solving the Electromagnetic Inverse Scattering Problem
• MUSIC‐Type Electromagnetic Imaging of a Collection of Small Three‐Dimensional Inclusions
• Two Numerical Methods for Recovering Small Inclusions from the Scattering Amplitude at a Fixed Frequency
• A MUSIC Algorithm for Locating Small Inclusions Buried in a Half-Space from the Scattering Amplitude at a Fixed Frequency
• The factorization method for Maxwell's equations
• The linear sampling method and the MUSIC algorithm
• Linear integral equations
• Acoustic and electromagnetic equations. Integral representations for harmonic problems

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