Related papers: The probe and enclosure methods for inverse obstac…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
A multilayered particle is illuminated by plane acoustic or electromagnetic waves of one or several frequencies. We consider the inverse scattering problem for the identification of the layers and of the refraction coefficients of the…
The inverse scattering problem from the multi-frequency backscattering data is a long-standing open problem. We advance the theory by proving a local uniqueness result. Moreover, we introduce a direct sampling method for quantitatively…
We consider inverse obstacle and transmission scattering problems where the source of the incident waves is located on a smooth closed surface that is a boundary of a domain located outside of the obstacle/inhomogeneity of the media. The…
The motivation of this work is an inverse problem for the acoustic wave equation, where an array of sensors probes an unknown medium with pulses and measures the scattered waves. The goal of the inversion is to determine from these…
This paper is concerned with inverse crack scattering problems for time-harmonic acoustic waves. We prove that a piecewise linear crack with the sound-soft boundary condition in two dimensions can be uniquely determined by the far-field…
Consider the problem of inverse scattering of time-harmonic point sources from an infinite, penetrable rough interface with bounded obstacles buried in the lower half-space, where the interface is assumed to be a local perturbation of a…
The aim of this paper is to establish the framework of the enclosure method for some class of inverse problems whose governing equations are given by parabolic equations with discontinuous coefficients. The framework is given by considering…
This paper develops an efficient numerical method for the inverse scattering problem of a time-harmonic plane wave incident on a perfectly reflecting random periodic structure. The method is based on a novel combination of the Monte Carlo…
We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…
In this paper, we consider the obstacle scattering problem for biharmonic equations with a Dirichlet boundary condition in both two and three dimensions. Some basic properties are first derived for the biharmonic scattering solutions, which…
This paper aims to solve numerically the two-dimensional inverse medium scattering problem with far-field data. This is a challenging task due to the severe ill-posedness and strong nonlinearity of the inverse problem. As already known, it…
Consider the time-harmonic acoustic scattering from a bounded penetrable obstacle imbedded in an isotropic homogeneous medium. The obstacle is supposed to possess a circular conic point or an edge point on the boundary in three dimensions…
Consider a time-harmonic elastic point source incident on a bounded obstacle which is embedded in an open space filled with a homogeneous and isotropic elastic medium. This paper is concerned with the inverse problem of recovering the…
In this paper we consider the inverse electromagnetic scattering for a cavity surrounded by an inhomogeneous medium in three dimensions. The measurements are scattered wave fields measured on some surface inside the cavity, where such…
In this paper, we consider the inverse problem of determining the location and the shape of a sound-soft obstacle from the modulus of the far-field data for a single incident plane wave. By adding a reference ball artificially to the…
The time domain enclosure method is one of analytical methods for inverse obstacle problems governed by partial differential equations in the time domain. This paper considers the case when the governing equation is given by the Maxwell…
We consider the Bayesian approach to the inverse problem of recovering the shape of an object from measurements of its scattered acoustic field. Working in the time-harmonic setting, we focus on a Helmholtz transmission problem and then…
In inverse scattering problems, a model that allows for the simultaneous recovery of both the domain shape and an impedance boundary condition covers a wide range of problems with impenetrable domains, including recovering the shape of…
This paper is about perfectly electrically conducting structures designed to produce negligible scattered power when exposed to a time-harmonic plane electromagnetic wave. The structures feature cavities capable of concealing objects.…