Inverse medium scattering for the Helmholtz equation at fixed frequency

@article{Bao2005InverseMS,
  title={Inverse medium scattering for the Helmholtz equation at fixed frequency},
  author={Gang Bao and Peijun Li},
  journal={Inverse Problems},
  year={2005},
  volume={21},
  pages={1621 - 1641}
}
Consider a time-harmonic electromagnetic plane wave incident on a medium enclosed by a bounded domain in . In this paper, existence and uniqueness of the variational problem for the direct scattering are established. An energy estimate for the scattered field is obtained on which the Born approximation is based. The Fréchet differentiability of the scattering map is examined. A new continuation method for the inverse medium scattering, which reconstructs the scatterer of an inhomogeneous medium… 
View on IOP Publishing
math.purdue.edu
70 Citations
Highly Influential Citations
5
Background Citations
24
Methods Citations
21
Results Citations
2

70 Citations

Numerical solution of an inverse medium scattering problem for Maxwell's Equations at fixed frequency

Recent Studies on Inverse Medium Scattering Problems

Regularized recursive linearization methods are presented for solving a two-dimensional inverse medium scattering problem, which reconstructs the scatterer of an inhomogeneous medium from the…

COMPUTATIONAL INVERSE MEDIUM SCATTERING AT FIXED FREQUENCY

A continuation method is presented for solving the inverse medium scattering problem of the Helmholtz equation in R. The algorithm requires only single-frequency scattering data. Using an initial…

Multifrequency Iterative Methods for the Inverse Medium Scattering Problems in Elasticity

The direct scattering problem is reduced to an equivalent system on a bounded domain by introducing an exact transparent boundary condition and the wellposedness of the corresponding variational problem is established.

An efficient method for the solution of the inverse scattering problem for penetrable obstacles

Inverse scattering by a continuation method with initial guesses from a direct imaging algorithm

Inverse medium scattering from periodic structures with fixed-direction incoming waves

This paper is concerned with inverse time-harmonic acoustic and electromagnetic scattering from an infinite biperiodic medium (diffraction grating) in three dimensions. In the acoustic case, we prove…

Near-field imaging of periodic inhomogeneous media

This paper is concerned with the inverse electromagnetic scattering problem by a periodic structure in the two-dimensional transverse electric (TE) polarization case. The structure is assumed to…

On the inverse scattering problem for radially-symmetric domains in two dimensions

A method for solving inverse problems for the Helmholtz equation in radially-symmetric domains given multi-frequency data based on the construction of suitable trace formulas which relate the impedance of the total field at multiple frequencies to derivatives of the potential.

Infinite-dimensional Bayesian approach for inverse scattering problems of a fractional Helmholtz equation

...

References

SHOWING 1-10 OF 18 REFERENCES

Inverse Medium Scattering Problems for Electromagnetic Waves

In this paper, existence and uniqueness of the variational problem for forward scattering are established and an energy estimate for the scattered field with a uniform bound with respect to the wavenumber is obtained in the case of low frequency on which the Born approximation is based.

Inverse scattering via Heisenberg's uncertainty principle

We present a stable method for the fully nonlinear inverse scattering problem of the Helmholtz equation in two dimensions. The new approach is based on the observation that ill-posedness of the…

Numerical Solution of Inverse Scattering Problems with Multi-experimental Limited Aperture Data

A regularized homotopy continuation method is presented for numerical solution of nonlinear ill-posedness inverse problems and the convergence of the iterative method is examined by numerical examples.

Regularity and Stability for the Scattering Map of a Linearized Inverse Medium Problem

The main goal of this paper is to study the linearization of an inverse medium problem. Regularity and stability results are established for the near-field scattering map (or scattering matrix) which…

Generalized linear inversion and the first Born theory for acoustic media

A procedure is derived which incorporates a generalized linear inverse viewpoint within a multidimensional Born inversion method. The method we present is a more general Born theory which can…

Near Field Microscopy and Near Field Optics

The early eighties have experienced a revolution in the perception of physical phenomena. This revolution is the birth of a new generation of imaging systems based on the detection of non-radiating…

Elliptic Partial Differential Equa-tions of Second Order

Chapter 1. Introduction Part I: Linear Equations Chapter 2. Laplace's Equation 2.1 The Mean Value Inequalities 2.2 Maximum and Minimum Principle 2.3 The Harnack Inequality 2.4 Green's Representation…

Regularization of Inverse Problems

Preface. 1. Introduction: Examples of Inverse Problems. 2. Ill-Posed Linear Operator Equations. 3. Regularization Operators. 4. Continuous Regularization Methods. 5. Tikhonov Regularization. 6.…

Near-Field Tomography

We consider the inverse scattering problem for wave fields containing evanescent components. Applications to near-field optics and tomographic imaging with subwavelength resolution are described.

Three-dimensional total internal reflection microscopy.

An analytic solution to this problem within the weak-scattering approximation is used to develop a novel form of three-dimensional microscopy with subwavelength resolution.