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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…
The goal of this paper is to reconstruct spatially distributed dielectric constants from complex-valued scattered wave field by solving a 3D coefficient inverse problem for the Helmholtz equation at multi-frequencies. The data are generated…
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…
The problem to be studied in this work is within the context of coefficient identification problems for the wave equation. More precisely, we consider the problem of reconstruction of the refractive index (or equivalently, the dielectric…
This paper addresses a factorization method for imaging the support of a wave-number-dependent source function from multi-frequency data measured at a finite pair of symmetric receivers in opposite directions. The source function is given…
This paper is concerned with the multi-frequency factorization method for imaging the support of a wave-number-dependent source function. It is supposed that the source function is given by the inverse Fourier transform of some…
In this paper, a reconstruction method for the spatially distributed dielectric constant of a medium from the back scattering wave field in the frequency domain is considered. Our approach is to propose a globally convergent algorithm,…
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,…
This paper is concerned with an inverse wavenumber/frequency-dependent source problem for the Helmholtz equation. In two and three dimensions, the unknown source term is supposed to be compactly supported in spatial variables but…
This paper introduces a hybrid computational framework for the multi-frequency inverse source problem governed by the Helmholtz equation. By integrating a classical Fourier method with a deep convolutional neural network, we address the…
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…
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…
This work is concerned with an inverse problem of identifying the current source distribution of the time-harmonic Maxwell's equations from multi-frequency measurements. Motivated by the Fourier method for the scalar Helmholtz equation and…
We propose in this paper a globally numerical method to solve a phaseless coefficient inverse problem: how to reconstruct the spatially distributed refractive index of scatterers from the intensity (modulus square) of the full complex…
A new numerical method to solve an inverse source problem for the Helmholtz equation in inhomogenous media is proposed. This method reduces the original inverse problem to a boundary value problem for a coupled system of elliptic PDEs, in…
This paper is concerned with a numerical method for a 3D coefficient inverse problem with phaseless scattering data. These are multi-frequency data generated by a single direction of the incident plane wave. Our numerical procedure consists…
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…
This paper investigates inverse source problems for time-dependent electromagnetic waves governed by Maxwell's equations. After applying the Fourier transform with respect to time, the problem leads to a frequency-domain electromagnetic…
We consider the multi-frequency inverse source problem for the scalar Helmholtz equation in the plane. The goal is to reconstruct the source term in the equation from measurements of the solution on a surface outside the support of the…
In this paper, we show for the first time the increasing stability of the inverse source problem for the n-dimensional Helmholtz equation at multiple wave numbers, which is different from the two-or three-dimensional Helmholtz equation. In…