Related papers: A Two-stage Method for Inverse Medium Scattering
This paper addresses the challenging and interesting inverse problem of reconstructing the spatially varying dielectric constant of a medium from phaseless backscattering measurements generated by single-point illumination. The underlying…
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…
Time-harmonic acoustic inverse scattering concerns the ill-posed and nonlinear problem of determining the refractive index of an inaccessible, penetrable scatterer based on far field wave scattering data. When the scattering is weak, the…
We consider the inverse scattering problem to reconstruct a local perturbation of a given inhomogeneous periodic layer in $\mathbb{R}^d$, $d=2,3$, using near field measurements of the scattered wave on an open set of the boundary above the…
We propose a data-assisted two-stage method for solving an inverse random source problem of the Helmholtz equation. In the first stage, the regularized Kaczmarz method is employed to generate initial approximations of the mean and variance…
We propose a method to reconstruct the optical properties of a scattering medium with subwavelength resolution. The method is based on the solution to the inverse scattering problem with photoactivated internal sources. Numerical…
This paper is concerned with inverse scattering problems of determining the support of an isotropic and homogeneous penetrable body from knowledge of multi-static far-field patterns in acoustics and in linear elasticity. The normal…
We analyze the inverse problem to reconstruct the shape of a three dimensional homogeneous dielectric obstacle from the knowledge of noisy far field data. The forward problem is solved by a system of second kind boundary integral equations.…
We consider the numerical solution of the scattering of time-harmonic plane waves from an infinite periodic array of reflection or transmission obstacles in a homogeneous background medium, in two dimensions. Boundary integral formulations…
The inverse scattering problems have been popular for the past thirty years. While very successful in many cases, progress has lagged when only {\em limited-aperture} measurement is available. In this paper, we perform some elementary study…
The solution of a multi-frequency 1d inverse medium problem consists of recovering the refractive index of a medium from measurements of the scattered waves for multiple frequencies. In this paper, rigorous stability estimates are derived…
Image reconstruction under multiple light scattering is crucial in a number of applications such as diffraction tomography. The reconstruction problem is often formulated as a nonconvex optimization, where a nonlinear measurement model is…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
We develop three inverse elastic scattering schemes for locating multiple small, extended and multiscale rigid bodies, respectively. There are some salient and promising features of the proposed methods. The cores of those schemes are…
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…
The article deals with a classical inverse problem: the computation of the refractive index of a medium from ultrasound time-of-flight (TOF) measurements. This problem is very popular in seismics but also for tomographic problems in…
An example of full solution of the inverse scattering problem on the half line is presented. For this purpose, a simple analytically solvable model system (Morse potential) is used, which is expected to be a reasonable approximation to a…
This paper presents a fast high-order method for the solution of two-dimensional problems of scattering by penetrable inhomogeneous media, with application to high-frequency configurations containing (possibly) discontinuous refractivities.…
Similar to the obstacle or medium scattering problems, an important property of the phaseless far field patterns for source scattering problems is the translation invariance. Thus it is impossible to reconstruct the location of the…
This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves from a penetrable and buried obstacles. By introducing a related transmission scattering problem, a Newton iteration method is proposed to…