Introduction.- The Helmholtz Equation.- Direct Acoustic Obstacle Scattering.- III-Posed Problems.- Inverse Acoustic Obstacle Scattering.- The Maxwell Equations.- Inverse Electromagnetic Obstacle Scattering.- Acoustic Waves in an Inhomogeneous Medium.- Electromagnetic Waves in an Inhomogeneous Medium.- The Inverse Medium Problem.-References.- Index

Inverse Acoustic and Electromagnetic Scattering Theory

Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

We show that the coefficient -y(x) of the elliptic equation Vie (QyVu) = 0 in a two-dimensional domain is uniquely determined by the corresponding Dirichlet-to-Neumann map on the boundary, and give a reconstruction pro

https://www.jstor.org/stable/pdfplus/2118653.pdf

Global uniqueness for a two-dimensional inverse boundary value problem

This paper is concerned with the development of an inversion scheme for two-dimensional inverse scattering problems in the resonance region which does not use nonlinear optimization methods and is relatively independent of the geometry and physical properties of the scatterer It is assumed that the far field pattern corresponding to observation angle and plane waves incident at angle is known for all  From this information, the support of the scattering obstacle is obtained by solving the integral equation where k is the wavenumber and is on a rectangular grid containing the scatterer The support is found by noting that is unbounded as approaches the boundary of the scattering object from inside the scatterer Numerical examples are given showing the practicality of this method

https://iopscience.iop.org/article/10.1088/0266-5611/12/4/003/pdf

A simple method for solving inverse scattering problems in the resonance region

We review theoretical and numerical studies of the inverse problem of electrical impedance tomography which seeks the electrical conductivity and permittivity inside a body, given simultaneous measurements of electrical currents and potentials at the boundary.

/pdf/electrical-impedance-tomography-3po2ct3t0v.pdf

Electrical impedance tomography

Global identifiability for an inverse problem for the Schrödinger equation in a magnetic field

We consider the question of whether one can determine the anisotropic, quasilinear conductivity of a medium by making voltage and current measurements at the boundary. We prove that all the known results for the linear case also hold in the quasilinear case.

Inverse problems in quasilinear anisotropic media

On a quasilinear inverse boundary value problem

We consider the Schrodinger operator for a magnetic potential A and an electric potential q, which are supported in a bounded domain in R n with n ≥ 3. We prove that knowledge of the Dirichlet to Neumann map associated to the Schrodinger operator determines the magnetic field rot(A) and the electric potential 4 simultaneously, provided rot(A) is small in the L∞ topology

/pdf/an-inverse-boundary-value-problem-for-schrodinger-operators-3hmmclxbw5.pdf

An inverse boundary value problem for Schrödinger operators with vector potentials

In this paper we considered several formally determined problems in two dimensions. There are no global identifiability results for these problems. However, we can recover an important feature of these functions, namely their singularities. More precisely, we prove that one can determine the location and strength of singularities of anL∞ compactly supported potential by knowing the associated scattering amplitude at a fixed energy. Also we prove that one can determine the location and strength of the singularities of the sound speed of a medium by making measurements just on the boundary of the medium.

/pdf/recovery-of-singularities-for-formally-determined-inverse-53q9q64rwx.pdf

Ziqi Sun

Papers

Global identifiability for an inverse problem for the Schrödinger equation in a magnetic field

Inverse problems in quasilinear anisotropic media

On a quasilinear inverse boundary value problem

An inverse boundary value problem for Schrödinger operators with vector potentials

Recovery of singularities for formally determined inverse problems