Related papers: Reconstructing electromagnetic obstacles by the en…
This letter announces and summarizes results obtained in arXiv:1111.5051 and considers several natural extensions. The aforementioned paper proposes a procedure to reconstruct coefficients in a second-order, scalar, elliptic equation from…
This work concerns inverse boundary value problems for the time-harmonic Maxwell's equations on differential $1-$forms. We formulate the boundary value problem on a $3-$dimensional compact and simply connected Riemannian manifold $M$ with…
Three papers describing different methods to solve the inverse scattering problem of the reconstruction of the shape and/or impedance of an obstacle have been chosen for analysis. This literature review consists of an evaluation of these…
We study the inverse conductivity problem of how to reconstruct an isotropic electrical conductivity distribution $\gamma$ in an object from static electrical measurements on the boundary of the object. We give an exact reconstruction…
We develop a novel wave imaging scheme for reconstructing the shape of an inhomogeneous scatterer and we consider the inverse acoustic obstacle scattering problem as a prototype model for our study. There exists a wealth of reconstruction…
Physics has played a fundamental role in medicine sciences, specially in imaging diagnostic. Currently, image reconstruction techniques are already taught in Physics courses and there is a growing interest in new potential applications. The…
A novel computational, non-iterative and noise-robust reconstruction method is introduced for the planar anisotropic inverse conductivity problem. The method is based on bypassing the unstable step of the reconstruction of the values of the…
This paper addresses the electromagnetic inverse scattering problem of determining the location and shape of anisotropic objects from near-field data. We investigate both cases involving the Helmholtz equation and Maxwell's equations for…
This paper gives a note on an application of the enclosure method to an inverse obstacle scattering problem governed by the Helmholtz equation in two dimensions. It is shown that one can uniquely determine the convex hull of an unknown…
We consider the time-harmonic elastic wave scattering from a general (possibly anisotropic) inhomogeneous medium with an embedded impenetrable obstacle. We show that the impenetrable obstacle can be effectively approximated by an isotropic…
Inverse problems are prevalent in numerous scientific and engineering disciplines, where the objective is to determine unknown parameters within a physical system using indirect measurements or observations. The inherent challenge lies in…
We present a new approach to three-dimensional electromagnetic scattering problems via fast isogeometric boundary element methods. Starting with an investigation of the theoretical setting around the electric field integral equation within…
We introduce a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$ - $\Omega$ a…
We introduce the EMC algorithm for reconstructing a particle's 3D diffraction intensity from very many photon shot-noise limited 2D measurements, when the particle orientation in each measurement is unknown. The algorithm combines 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…
A direct reconstruction algorithm based on Calder\'on's linearization method for the reconstruction of isotropic conductivities is proposed for anisotropic conductivities in two-dimensions. To overcome the non-uniqueness of the anisotropic…
Now a final and maybe simplest formulation of the enclosure method applied to inverse obstacle problems governed by partial differential equations in a {\it spacial domain with an outer boundary} over a finite time interval is fixed. The…
The state of art of electromagnetic integral equations has seen significant growth over the past few decades, overcoming some of the fundamental bottlenecks: computational complexity, low frequency and dense discretization breakdown,…
In this paper, we define a new problem of recovering the 3D geometry of an object confined in a transparent enclosure. We also propose a novel method for solving this challenging problem. Transparent enclosures pose challenges of multiple…
The goal of this work is to study the electromagnetic scattering problem of time-domain Maxwell's equations in an unbounded structure. An exact transparent boundary condition is developed to reformulate the scattering problem into an…