Related papers: Reconstruction of shapes and refractive indices fr…
We consider an inverse problem of reconstructing a degeneracy point in the diffusion coefficient in a one-dimensional parabolic equation by measuring the normal derivative on one side of the domain boundary. We analyze the sensitivity of…
We consider an inverse problem of reconstructing the conductivity function in a hyperbolic equation using single space-time domain noisy observations of the solution on the backscattering boundary of the computational domain. We formulate…
We analyze in this paper the performance of a newly developed globally convergent numerical method for a coefficient inverse problem for the case of multi-frequency experimental backscatter data associated to a single incident wave. These…
This paper concerns the reconstruction of a scalar diffusion coefficient $\sigma(x)$ from redundant functionals of the form $H_i(x)=\sigma^{2\alpha}(x)|\nabla u_i|^2(x)$ where $\alpha\in\Rm$ and $u_i$ is a solution of the elliptic problem…
The forward problem here is the Cauchy problem for a 1D hyperbolic PDE with a variable coefficient in the principal part of the operator. That coefficient is the spatially distributed dielectric constant. The inverse problem consists of the…
This paper is dedicated to design a direct sampling method of inverse electromagnetic scattering problems, which uses multi-frequency sparse backscattering far field data for reconstructing the boundary of perfectly conducting obstacles. We…
In this article, we consider the reconstruction of $\rho(t)$ in the (time-fractional) diffusion equation $(\partial_t^\alpha-\triangle)u(x,t)=\rho(t)g(x)$ ($0<\alpha \le 1$) by the observation at a single point $x_0$. We are mainly…
The aim of this article is to present a hybrid finite element/finite difference method which is used for reconstructions of electromagnetic properties within a realistic breast phantom. This is done by studying the mentioned properties'…
A 3-D inverse medium problem in the frequency domain is considered. Another name for this problem is Coefficient Inverse Problem. The goal is to reconstruct spatially distributed dielectric constants from scattering data. Potential…
This revisit gives a survey on the analytical methods for the inverse exponential Radon transform which has been investigated in the past three decades from both mathematical interests and medical applications such as nuclear medicine…
The focus of this paper is on the concurrent reconstruction of both the diffusion and potential coefficients present in an elliptic/parabolic equation, utilizing two internal measurements of the solutions. A decoupled algorithm is…
Refractive Index Tomography is the inverse problem of reconstructing the continuously-varying 3D refractive index in a scene using 2D projected image measurements. Although a purely refractive field is not directly visible, it bends light…
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…
We consider the inverse scattering problem for inhomogeneous media of compact support governed by the fractional s-Helmholtz equation, with $0<s<1$, in dimensions $d=1,2,3$. In particular, we study the determination of the support of 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 consider the problem of imaging of objects buried under the ground using backscattering experimental time dependent measurements generated by a single point source or one incident plane wave. In particular, we estimate dielectric…
This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal data. This theory finds applications in multi-wave imaging, greedy methods to…
We consider the imaging problem of the reconstruction of a three-dimensional object via optical diffraction tomography under the assumptions of the Born approximation. Our focus lies in the situation that a rigid object performs an…
This paper is concerned with the numerical solution to a 3D coefficient inverse problem for buried objects with multi-frequency experimental data. The measured data, which are associated with a single direction of an incident plane wave,…
In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…