Convexification for the Inversion of a Time Dependent Wave Front in a Heterogeneous Medium
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Publication:5233552
DOI10.1137/18M1236034zbMath1420.35470arXiv1812.11281MaRDI QIDQ5233552
Michael V. Klibanov, Wenlong Zhang, Jingzhi Li
Publication date: 11 September 2019
Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1812.11281
numerical examplesconvexificationCarleman estimatecoefficient inverse problemglobal strict convexity
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Cites Work
- Unnamed Item
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- Carleman weight functions for a globally convergent numerical method for ill-posed Cauchy problems for some quasilinear PDEs
- Enhanced multilevel linear sampling methods for inverse scattering problems
- Mathematical and statistical methods for multistatic imaging
- Qualitative methods in inverse scattering theory. An introduction
- Numerical solution of the multidimensional Gelfand-Levitan equation
- Fast Toeplitz linear system inversion for solving two-dimensional acoustic inverse problem
- Carleman estimates for coefficient inverse problems and numerical applications.
- Direct methods of solving multidimensional inverse hyperbolic problems.
- Convexification of a 3-D coefficient inverse scattering problem
- Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems
- The Concept of Heterogeneous Scattering Coefficients and Its Application in Inverse Medium Scattering
- Iterative methods for solving coefficient inverse problems of wave tomography in models with attenuation
- An iterative method for 2D inverse scattering problems by alternating reconstruction of medium properties and wavefields: theory and application to the inversion of elastic waveforms
- Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems
- A direct sampling method to an inverse medium scattering problem
- A decoupling-based imaging method for inverse medium scattering for Maxwell's equations
- Recovering multiscale buried anomalies in a two-layered medium
- Inversion of weighted Radon transforms via finite Fourier series weight approximations
- Uniform Strict Convexity of a Cost Functional for Three-Dimensional Inverse Scattering Problem
- Global Convexity in a Three-Dimensional Inverse Acoustic Problem
- Globally Strictly Convex Cost Functional for a 1-D Inverse Medium Scattering Problem with Experimental Data
- Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems
- Convexification of electrical impedance tomography with restricted Dirichlet-to-Neumann map data
- A new version of the convexification method for a 1D coefficient inverse problem with experimental data
- Convergent Algorithm Based on Carleman Estimates for the Recovery of a Potential in the Wave Equation
- Recovering Dielectric Constants of Explosives via a Globally Strictly Convex Cost Functional
- A multilevel model correction method for parameter identification
- A direct sampling method for inverse electromagnetic medium scattering
- Inverse acoustic and electromagnetic scattering theory
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