Related papers: A new version of the convexification method for a …
A version of the convexification globally convergent numerical method is constructed for a coefficient inverse problem for a wave-like partial differential equation. The presence of the Carleman Weight Function in the corresponding…
To compute the spatially distributed dielectric constant from the backscattering data, we study a coefficient inverse problem for a 1D hyperbolic equation. To solve the inverse problem, we establish a new version of Carleman estimate and…
A version of the convexification numerical method for a Coefficient Inverse Problem for a 1D hyperbolic PDE is presented. The data for this problem are generated by a single measurement event. This method converges globally. The most…
An inverse scattering problem for the 3D acoustic equation in time domain is considered. The unknown spatially distributed speed of sound is the subject of the solution of this problem. A single location of the point source is used. Using a…
A version of the so-called "convexification" numerical method for a coefficient inverse scattering problem for the 3D Hemholtz equation is developed analytically and tested numerically. Backscattering data are used, which result from a…
We present in this paper a novel numerical reconstruction method for solving a 3D coefficient inverse problem with scattering data generated by a single direction of the incident plane wave. This inverse problem is well-known to be a highly…
A new numerical method is proposed for a 1-D inverse medium scattering problem with multi-frequency data. This method is based on the construction of a weighted cost functional. The weight is a Carleman Weight Function (CWF). In other…
A convexification-based numerical method for a Coefficient Inverse Problem for a parabolic PDE is presented. The key element of this method is the presence of the so-called Carleman Weight Function in the numerical scheme. Convergence…
We propose a new approach to constructing globally strictly convex objective functional in a 1-D inverse medium scattering problem using multi-frequency backscattering data. The global convexity of the proposed objective functional is…
A Carleman Weight Function (CWF) is used to construct a new cost functional for a Coefficient Inverse Problems for a hyperbolic PDE. Given a bounded set of an arbitrary size in a certain Sobolev space, one can choose the parameter of the…
A coefficient inverse problem for a parabolic equation is considered. Using a Carleman Weight Function, a globally strictly convex cost functional is constructed for this problem.
It is shown that the contraction mapping principle with the involvement of a Carleman Weight Function works for a Coefficient Inverse Problem for a 1D hyperbolic equation. Using a Carleman estimate, the global convergence of the…
For the first time, we develop in this paper the globally convergent convexification numerical method for a Coefficient Inverse Problem for the 3D Helmholtz equation for the case when the backscattering data are generated by a point source…
Inverse scattering problems of the reconstructions of physical properties of a medium from boundary measurements are substantially challenging ones. This work aims to verify the performance on experimental data of a newly developed…
We propose a new globally convergent numerical method to solve Hamilton-Jacobi equations in $\mathbb{R}^d$, $d \geq 1$. This method is named as the Carleman convexification method. By Carleman convexification, we mean that we use a Carleman…
An $\left( n+1\right) -$D coefficient inverse problem for the radiative stationary transport equation is considered for the first time. A globally convergent so-called convexification numerical \ method is developed and its convergence…
A Coefficient Inverse Problem for the radiative transport equation is considered. The globally convergent numerical method, the so-called convexification, is developed. For the first time, the viscosity solution is considered for a boundary…
In this paper, a new semi-discrete version of the Carleman estimate-based convexification globally convergent numerical method is developed. It is used for the delivery of the starting point for the training procedure of deep learning. An…
The inverse problem of estimating dielectric constants of explosives using boundary measurements of one component of the scattered electric field is addressed. It is formulated as a coefficient inverse problem for a hyperbolic differential…
This paper is concerned with the convergence of a series associated with a certain version of the convexification method. That version has been recently developed by the research group of the first author for solving coefficient inverse…