52 citations · 122 across the 13 of their papers we have counts for
13 papers
A globally convergent numerical method for a 3D coefficient inverse problem for a wave-like equation
Michael V. Klibanov, Jingzhi Li, Wenlong Zhang
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 o…
A data-driven model reduction method for parabolic inverse source problems and its convergence analysis
Zhongjian Wang, Wenlong Zhang, Zhiwen Zhang
In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems efficiently. Our method consists of offline and online stages. In the off-…
Stochastic convergence of regularized solutions and their finite element approximations to inverse source problems
Zhiming Chen, Wenlong Zhang, Jun Zou
In this work, we investigate the regularized solutions and their finite element solutions to the inverse source problems governed by partial differential equations, and establish t…
Linear Lavrent'ev Integral Equation for the Numerical Solution of a Nonlinear Coefficient Inverse Problem
Michael V. Klibanov, Jingzhi Li, Wenlong Zhang
For the first time, we develop a convergent numerical method for the llinear integral equation derived by M.M. Lavrent'ev in 1964 with the goal to solve a coefficient inverse probl…
Convexification for an Inverse Parabolic Problem
Michael V. Klibanov, Jingzhi Li, Wenlong Zhang
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 Carlema…
Convexification for the inversion of a time dependent wave front in a heterogeneous medium
Michael V. Klibanov, Jingzhi Li, Wenlong Zhang
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 pro…
Linearized Reconstruction for Diffuse Optical Spectroscopic Imaging
Habib Ammari, Bangti Jin, Wenlong Zhang
In this paper, we present a novel reconstruction method for diffuse optical spectroscopic imaging with a commonly used tissue model of optical absorption and scattering. It is base…
Electrical Impedance Tomography with Restricted Dirichlet-to-Neumann Map Data
Michael V. Klibanov, Jingzhi Li, Wenlong Zhang
We propose a new numerical method to reconstruct the isotropic electrical conductivity from measured restricted Dirichlet-to-Neumann map data in electrical impedance tomography (EI…
A finite element method for elliptic problems with observational boundary data
Zhiming Chen, Rui Tuo, Wenlong Zhang
In this paper we propose a finite element method for solving elliptic equations with the observational Dirichlet boundary data which may subject to random noises. The method is bas…
Determining anisotropic conductivity using diffusion tensor imaging data in magneto-acoustic tomography with magnetic induction
Habib Ammari, Lingyun Qiu, Fadil Santosa +1
In this paper we present a mathematical and numerical framework for a procedure of imaging anisotropic electrical conductivity tensor by integrating magneto-acoutic tomography with…
Stochastic Convergence of A Nonconforming Finite Element Method for the Thin Plate Spline Smoother for Observational Data
Zhiming Chen, Rui Tuo, Wenlong Zhang
The thin plate spline smoother is a classical model for fnding a smooth function from the knowledge of its observation at scattered locations which may have random noises. We consi…
Towards monitoring critical microscopic parameters for electropermeabilization
Habib Ammari, Thomas Widlak, Wenlong Zhang
Electropermeabilization is a clinical technique in cancer treatment to locally stimulate the cell metabolism. It is based on electrical fields that change the properties of the cel…
The Linearized Inverse Problem in Multifrequency Electrical Impedance Tomography
Giovanni S. Alberti, Habib Ammari, Bangti Jin +2
This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finit…