Globally Strictly Convex Cost Functional for a 1-D Inverse Medium Scattering Problem with Experimental Data
From MaRDI portal
Publication:4588204
DOI10.1137/17M1122487zbMath1373.35337arXiv1703.08158MaRDI QIDQ4588204
Michael V. Klibanov, Anders Sullivan, Aleksandr E. Kolesov, Lam H. Nguyen
Publication date: 1 November 2017
Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1703.08158
Related Items (28)
Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data ⋮ Convexity of a discrete Carleman weighted objective functional in an inverse medium scattering problem ⋮ Solving a 1-D inverse medium scattering problem using a new multi-frequency globally strictly convex objective functional ⋮ Recovery of a Smooth Metric via Wave Field and Coordinate Transformation Reconstruction ⋮ Exact boundary controllability of 1D semilinear wave equations through a constructive approach ⋮ Exact controllability of semilinear heat equations through a constructive approach ⋮ Convexification and experimental data for a 3D inverse scattering problem with the moving point source ⋮ A method of solving the coefficient inverse problems of wave tomography ⋮ Convexification of a 3-D coefficient inverse scattering problem ⋮ Convexification-based globally convergent numerical method for a 1D coefficient inverse problem with experimental data ⋮ Convexification for an inverse problem for a 1D wave equation with experimental data ⋮ A Coefficient Inverse Problem with a Single Measurement of Phaseless Scattering Data ⋮ Convexification of electrical impedance tomography with restricted Dirichlet-to-Neumann map data ⋮ An inverse space-dependent source problem for hyperbolic equations and the Lipschitz-like convergence of the quasi-reversibility method ⋮ Inverse scattering for the one-dimensional Helmholtz equation with piecewise constant wave speed ⋮ On convexity of the functional for inverse problems of hyperbolic equations ⋮ A new version of the convexification method for a 1D coefficient inverse problem with experimental data ⋮ Convergent numerical methods for parabolic equations with reversed time via a new Carleman estimate ⋮ A Numerical Method to Solve a Phaseless Coefficient Inverse Problem from a Single Measurement of Experimental Data ⋮ Unique continuation for a reaction-diffusion system with cross diffusion ⋮ On the travel time tomography problem in 3D ⋮ Convexification for the Inversion of a Time Dependent Wave Front in a Heterogeneous Medium ⋮ Inverse coefficient problems for a transport equation by local Carleman estimate ⋮ Direct and inverse scalar scattering problems for the Helmholtz equation in \(\mathbb{R}^m\) ⋮ The two-step method for determining a piecewise-continuous refractive index of a 2D scatterer by near field measurements ⋮ Non-iterative two-step method for solving scalar inverse 3D diffraction problem ⋮ Reconstruction of contact regions in semiconductor transistors using Dirichlet-Neumann cost functional approach ⋮ On the stability of recovering two sources and initial status in a stochastic hyperbolic-parabolic system
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The factorization method for the Drude-Born-Fedorov model for periodic chiral structures
- Carleman weight functions for a globally convergent numerical method for ill-posed Cauchy problems for some quasilinear PDEs
- A globally convergent numerical method for a 1-d inverse medium problem with experimental data
- Globally strongly convex cost functional for a coefficient inverse problem
- Multidimensional inverse spectral problem for the equation \(-\Delta \psi -(v(x)-Eu(x))\psi =0\)
- Numerical solution of the multidimensional Gelfand-Levitan equation
- The inverse scattering problem on a fixed energy level for two- dimensional Schrödinger operator
- Global optimization methods for multimodal inverse problems
- Numerical solution of a coefficient inverse problem with multi-frequency experimental raw data by a globally convergent algorithm
- Reconstruction of small inhomogeneities from boundary measurements
- Carleman estimates for coefficient inverse problems and numerical applications.
- Inverse acoustic obstacle scattering problems using multifrequency measurements
- The Krein method and the globally convergent method for experimental data
- Numerical solution of an ill-posed Cauchy problem for a quasilinear parabolic equation using a Carleman weight function
- Globally strictly convex cost functional for an inverse parabolic problem
- Phased and Phaseless Domain Reconstructions in the Inverse Scattering Problem via Scattering Coefficients
- Global Carleman Estimates for Waves and Applications
- Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems
- Supercomputer technologies in inverse problems of ultrasound tomography
- Riemann–Hilbert problem approach for two-dimensional flow inverse scattering
- Iterative methods for solving coefficient inverse problems of wave tomography in models with attenuation
- Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems
- Blind backscattering experimental data collected in the field and an approximately globally convergent inverse algorithm
- Inverse scattering problems with multi-frequencies
- Carleman weight functions for solving ill-posed Cauchy problems for quasilinear PDEs
- On the Accuracy of the Numerical Detection of Complex Obstacles from Far Field Data Using the Probe Method
- Uniform Strict Convexity of a Cost Functional for Three-Dimensional Inverse Scattering Problem
- Global Convexity in a Three-Dimensional Inverse Acoustic Problem
- The linear sampling method for the transmission problem in three-dimensional linear elasticity
- Convergent Algorithm Based on Carleman Estimates for the Recovery of a Potential in the Wave Equation
- A numerical method for reconstructing the coefficient in a wave equation
- A Globally Convergent Numerical Method for a Coefficient Inverse Problem
- Regularized recursive Newton-type methods for inverse scattering problems using multifrequency measurements
- Imaging of Buried Objects from Experimental Backscattering Time-Dependent Measurements Using a Globally Convergent Inverse Algorithm
- An iterative approach to non-overdetermined inverse scattering at fixed energy
- Locating Multiple Multiscale Acoustic Scatterers
- Recovering Dielectric Constants of Explosives via a Globally Strictly Convex Cost Functional
- A direct sampling method for inverse electromagnetic medium scattering
This page was built for publication: Globally Strictly Convex Cost Functional for a 1-D Inverse Medium Scattering Problem with Experimental Data
