44 citations · 334 across the 44 of their papers we have counts for
30 papers · 1 filter
A Carleman-Picard approach for reconstructing zero-order coefficients in parabolic equations with limited data
Ray Abney, Thuy T. Le, Loc H. Nguyen +1
We propose a globally convergent computational technique for the nonlinear inverse problem of reconstructing the zero-order coefficient in a parabolic equation using partial bounda…
Numerical verification of the convexification method for a frequency-dependent inverse scattering problem with experimental data
Thuy Le, Vo Anh Khoa, Michael Victor Klibanov +3
The reconstruction of physical properties of a medium from boundary measurements, known as inverse scattering problems, presents significant challenges. The present study aims to v…
Numerical differentiation by the polynomial-exponential basis
Phuong M. Nguyen, Thuy T. Le, Loc H. Nguyen +1
Our objective is to calculate the derivatives of data corrupted by noise. This is a challenging task as even small amounts of noise can result in significant errors in the computat…
Convexification Numerical Method for a Coefficient Inverse Problem for the Riemannian Radiative Transfer Equation
Michael V. Klibanov, Jingzhi Li, Loc H. Nguyen +2
The first globally convergent numerical method for a Coefficient Inverse Problem (CIP) for the Riemannian Radiative Transfer Equation (RRTE) is constructed. This is a version of th…
Reconstructing a space-dependent source term via the quasi-reversibility method
Loc H. Nguyen, Huong T. Vu
The aim of this paper is to solve an important inverse source problem which arises from the well-known inverse scattering problem. We propose to truncate the Fourier series of the…
The Carleman-Newton method to globally reconstruct a source term for nonlinear parabolic equation
Anuj Abhishek, Thuy Le, Loc Nguyen +1
We propose to combine the Carleman estimate and the Newton method to solve an inverse source problem for nonlinear parabolic equations from lateral boundary data. The stability of…
Convexification for a CIP for the RTE]{Convexification Numerical Method for a Coefficient Inverse Problem for the Radiative Transport Equation
Michael V. Klibanov, Jingzhi Li, Loc H. Nguyen +1
An D coefficient inverse problem for the radiative stationary transport equation is considered for the first time. A globally convergent so-called convexificat…
Numerical reconstruction for 3D nonlinear SAR imaging via a version of the convexification method
Vo Anh Khoa, Michael Victor Klibanov, William Grayson Powell +1
This work extends the applicability of our recent convexification-based algorithm for constructing images of the dielectric constant of buried or occluded target. We are orientated…
The Carleman-based contraction principle to reconstruct the potential of nonlinear hyperbolic equations
Dinh-Liem Nguyen, Loc Nguyen, Trung Truong
We develop an efficient and convergent numerical method for solving the inverse problem of determining the potential of nonlinear hyperbolic equations from lateral Cauchy data. In…
The Carleman contraction mapping method for quasilinear elliptic equations with over-determined boundary data
Loc Hoang Nguyen
We propose a globally convergent numerical method to compute solutions to a general class of quasi-linear PDEs with both Neumann and Dirichlet boundary conditions. Combining the qu…
Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data
Thuy T. Le, Michael V. Klibanov, Loc H. Nguyen +2
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…
A Carleman-based numerical method for quasilinear elliptic equations with over-determined boundary data and applications
Thuy T. Le, Loc H. Nguyen, Hung V. Tran
We propose a new iterative scheme to compute the numerical solution to an over-determined boundary value problem for a general quasilinear elliptic PDE. The main idea is to repeate…
Convexification-based globally convergent numerical method for a 1D coefficient inverse problem with experimental data
Michael V. Klibanov, Thuy T. Le, Loc H. Nguyen +2
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 pro…
Numerical viscosity solutions to Hamilton-Jacobi equations via a Carleman estimate and the convexification method
Michael Klibanov, Loc H. Nguyen, Hung V. Tran
We propose a globally convergent numerical method, called the convexification, to numerically compute the viscosity solution to first-order Hamilton-Jacobi equations through the va…
Convexification inversion method for nonlinear SAR imaging with experimentally collected data
M. V. Klibanov, V. A. Khoa, A. V. Smirnov +4
This paper is concerned with the study of a version of the globally convergent convexification method with direct application to synthetic aperture radar (SAR) imaging. Results of…
The gradient descent method for the convexification to solve boundary value problems of quasi-linear PDEs and a coefficient inverse problem
Thuy T. Le, Loc. H. Nguyen
We study the global convergence of the gradient descent method of the minimization of strictly convex functionals on an open and bounded set of a Hilbert space. Such results are un…
The quasi-reversibility method to numerically solve an inverse source problem for hyperbolic equations
Thuy T. Le, Loc H. Nguyen, Thi-Phong Nguyen +1
We propose a numerical method to solve an inverse source problem of computing the initial condition of hyperbolic equations from the measurements of Cauchy data. This problem arise…
An inverse problem of a simultaneous reconstruction of the dielectric constant and conductivity from experimental backscattering data
Vo Anh Khoa, Grant W. Bidney, Michael V. Klibanov +4
This report extends our recent progress in tackling a challenging 3D inverse scattering problem governed by the Helmholtz equation. Our target application is to reconstruct dielect…
Convexification and experimental data for a 3D inverse scattering problem with the moving point source
Vo Anh Khoa, Grant W. Bidney, Michael V. Klibanov +4
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 pe…
Convexification for a 1D Hyperbolic Coefficient Inverse Problem with Single Measurement Data
Alexey V. Smirnov, Michael V. Klibanov, Loc H. Nguyen
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 measur…
Convergent numerical method for a linearized travel time tomography problem with incomplete data
Michael V. Klibanov, Thuy T. Le, Loc H. Nguyen
We propose a new numerical method to solve the linearized problem of travel time tomography with incomplete data. Our method is based on the technique of the truncation of the Four…
Convexification for a 3D inverse scattering problem with the moving point source
Vo Anh Khoa, Michael Victor Klibanov, Loc Hoang Nguyen
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 w…
On an inverse source problem for the full radiative transfer equation with incomplete data
Alexey V. Smirnov, Michael V. Klibanov, Loc H. Nguyen
A new numerical method to solve an inverse source problem for the radiative transfer equation involving the absorption and scattering terms, with incomplete data, is proposed. No r…
PDE-based numerical method for a limited angle X-ray tomography
Michael V. Klibanov, Loc H. Nguyen
A new numerical method for X-ray tomography for a specific case of incomplete Radon data is proposed. Potential applications are in checking out bulky luggage in airports. This met…