Looking Back on Inverse Scattering Theory
From MaRDI portal
Publication:4554899
DOI10.1137/17M1144763zbMath1402.35090OpenAlexW2899964107WikidataQ128981544 ScholiaQ128981544MaRDI QIDQ4554899
Publication date: 12 November 2018
Published in: SIAM Review (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/17m1144763
Scattering theory for PDEs (35P25) Ill-posed problems for PDEs (35R25) Inverse problems for PDEs (35R30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02)
Related Items
Reconstruction for shape and impedance in an inverse scattering problem, On local and global structures of transmission eigenfunctions and beyond, Simultaneous recovery of an obstacle and its excitation sources from near-field scattering data, An Accelerated Level-Set Method for Inverse Scattering Problems, Localized Sensitivity Analysis at High-Curvature Boundary Points of Reconstructing Inclusions in Transmission Problems, Stable determination of an elastic medium scatterer by a single far-field measurement and beyond, Machine learning based data retrieval for inverse scattering problems with incomplete data, A direct imaging method for the exterior and interior inverse scattering problems, The Linear Sampling Method for Random Sources, Geometrical Characterizations of Non-Radiating Sources at Polyhedral and Conical Corners with Applications, On nodal and generalized singular structures of Laplacian eigenfunctions and applications to inverse scattering problems, Two single-measurement uniqueness results for inverse scattering problems within polyhedral geometries, Some recent progress on inverse scattering problems within general polyhedral geometry, Some recent developments in the unique determinations in phaseless inverse acoustic scattering theory, On a local geometric property of the generalized elastic transmission eigenfunctions and application, On generalized Holmgren's principle to the Lamé operator with applications to inverse elastic problems, Comparison of shape derivatives using CutFEM for ill-posed Bernoulli free boundary problem, On vanishing and localizing around corners of electromagnetic transmission resonances, On vanishing near corners of conductive transmission eigenfunctions, A neural network scheme for recovering scattering obstacles with limited phaseless far-field data, Unique continuation from a generalized impedance edge-corner for Maxwell’s system and applications to inverse problems, On Novel Geometric Structures of Laplacian Eigenfunctions in $\mathbb{R}^3$ and Applications to Inverse Problems, On Geometrical Properties of Electromagnetic Transmission Eigenfunctions and Artificial Mirage
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A global uniqueness theorem for an inverse boundary value problem
- Multidimensional inverse spectral problem for the equation \(-\Delta \psi -(v(x)-Eu(x))\psi =0\)
- Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
- Reconstructions from boundary measurements
- A modified gradient method for two-dimensional problems in tomography
- The uniqueness of a solution to an inverse scattering problem for electromagnetic waves
- An inverse boundary value problem in electrodynamics
- Stability estimates and reconstructions in inverse acoustic scattering using singular sources
- On the uniqueness of the shape of a penetrable, anisotropic obstacle
- The linear sampling method revisited
- High-frequency approximation of the interior Dirichlet-to-Neumann map and applications to the transmission eigenvalues
- A hybrid method for inverse scattering for sound-soft obstacles in \(\mathbb R^3\)
- Fast methods for three-dimensional inverse obstacle scattering problems
- Fast numerical solution of the electromagnetic medium scattering problem and applications to the inverse problem
- New Stability Estimates for the Inverse Acoustic Inhomogeneous Medium Problem and Applications
- A level set method for inverse problems
- On the numerical solution of a three-dimensional inverse medium scattering problem
- Inverse Modeling
- Material derivatives of boundary integral operators in electromagnetism and application to inverse scattering problems
- Inverse Scattering Theory and Transmission Eigenvalues
- Acoustic inverse scattering using topological derivative of far-field measurements-based L 2 cost functionals
- Ellipticity in the Interior Transmission Problem in Anisotropic Media
- Sharp Weyl Law for Signed Counting Function of Positive Interior Transmission Eigenvalues
- Remarks on the Born approximation and the Factorization Method
- The Linear Sampling Method in Inverse Electromagnetic Scattering
- The Existence of an Infinite Discrete Set of Transmission Eigenvalues
- A level-set approach for inverse problems involving obstacles Fadil SANTOSA
- Uniqueness Theorems for the Inverse Problem of Acoustic Scattering
- On uniqueness in th invese transmission scattering problem
- The Interior Transmission Problem and Inverse Scattering from Inhomogeneous Media
- Inverse scattering problems with multi-frequencies
- Shape Identification in Inverse Medium Scattering Problems with a Single Far-Field Pattern
- Convergence and stability of the inverse scattering series for diffuse waves
- Transmission Eigenvalues
- Level set methods for inverse scattering—some recent developments
- Dense Sets and Far Field Patterns in Acoustic Wave Propagation
- THE INVERSE SCATTERING PROBLEM FOR TIME-HARMONIC ACOUSTIC WAVES IN AN INHOMOGENEOUS MEDIUM
- The Denseness of the Far Field Patterns for the Transmission Problem
- An inverse transmission problem for the Helmholtz equation
- The Inverse Problem of Acoustic Scattering
- The domain derivative and two applications in inverse scattering theory
- Reconstruction of an obstacle from the scattering amplitude at a fixed frequency
- Characterization of the shape of a scattering obstacle using the spectral data of the far field operator
- On the Topological Derivative in Shape Optimization
- Factorization of the far-field operator for the inhomogeneous medium case and an application in inverse scattering theory
- On the Far Field in Obstacle Scattering
- A uniqueness theorem for a transmission problem in inverse electromagnetic scattering
- Frechet differentiability of boundary integral operators in inverse acoustic scattering
- Iterative method for multi-dimensional inverse scattering problems at fixed frequencies
- Inverse scattering from an open arc
- Inverse scattering via Heisenberg's uncertainty principle
- Inverse obstacle problem: local uniqueness for rougher obstacles and the identification of a ball
- On the inverse acoustic scattering problem by an open arc: the sound-hard case
- A simple method using Morozov's discrepancy principle for solving inverse scattering problems
- Reconstruction of the three-dimensional refractive index in electromagnetic scattering by using a propagation backpropagation method
- The scattering support
- Newton s method for inverse obstacle scattering meets the method of least squares
- Uniqueness in an inverse scattering problem within non-trapping polygonal obstacles with at most two incoming waves
- Why linear sampling works
- A UNIQUENESS THEOREM FOR AN INVERSE ELECTROMAGNETIC SCATTERING PROBLEM IN INHOMOGENEOUS ANISOTROPIC MEDIA
- Newton-Kantorovitch algorithm applied to an electromagnetic inverse problem
- The linear sampling method for solving the electromagnetic inverse medium problem
- Parabolic transmission eigenvalue-free regions in the degenerate isotropic case
- Determining a sound-soft polyhedral scatterer by a single far-field measurement
- Uniqueness in inverse obstacle scattering (acoustics)
- A simple method for solving inverse scattering problems in the resonance region
- A fast new method to solve inverse scattering problems
- Far-Field Patterns for Acoustic Waves in an Inhomogeneous Medium
- Optimisation methods for an inverse problem with time-harmonic electromagnetic waves: an inverse problem in electromagnetic scattering
- On the solution of three-dimensional inverse obstacle acoustic scattering problems by a regularized Newton method
- On the Fréchet Derivative for Obstacle Scattering with an Impedance Boundary Condition
- A propagation-backpropagation method for ultrasound tomography
- An inverse problem for the Helmholtz equation
- On the Fréchet Derivative in Elastic Obstacle Scattering
- Uniqueness in an inverse acoustic obstacle scattering problem for both sound-hard and sound-soft polyhedral scatterers
- Inverse Medium Scattering Problems for Electromagnetic Waves
- Integral Equation Methods in Scattering Theory
- A generalized formulation of the linear sampling method with exact characterization of targets in terms of farfield measurements
- Reconstruction of an acoustically sound-soft obstacle from one incident field and the far-field pattern
- Reflection principle for the Maxwell equations and its application to inverse electromagnetic scattering
- Recovering a potential from Cauchy data in the two-dimensional case
- Notions of support for far fields
- Local uniqueness for the inverse scattering problem in acoustics via the Faber–Krahn inequality
- Nonlinear integral equations and the iterative solution for an inverse boundary value problem
- A new method in inverse scattering based on the topological derivative
- Inverse acoustic and electromagnetic scattering theory
- Recovery of the potential from fixed-energy scattering data