Globally convergent and adaptive finite element methods in imaging of buried objects from experimental backscattering radar measurements

DOI10.1016/j.cam.2014.11.055zbMath1332.78020arXiv1409.1167OpenAlexW2153242883MaRDI QIDQ2352327

John Bondestam Malmberg, Larisa Beilina, Michael V. Klibanov, Nguyen Trung Thành

Publication date: 30 June 2015

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.1167

zbMATH Keywords

adaptive finite element methodinverse scatteringglobally convergent algorithmrefractive indices

Mathematics Subject Classification ID

Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46) Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs (65M30)

Related Items (15)

Inverse coefficient problems for a first order hyperbolic system ⋮ Nanostructures imaging via numerical solution of a 3-D inverse scattering problem without the phase information ⋮ Mathematical Design of a Novel Gesture-Based Instruction/Input Device Using Wave Detection ⋮ On the Maxwell-wave equation coupling problem and its explicit finite-element solution. ⋮ A neural network warm-start approach for the inverse acoustic obstacle scattering problem ⋮ Convergence of Stabilized P1 Finite Element Scheme for Time Harmonic Maxwell’s Equations ⋮ Convergence of Explicit $$P_1$$ Finite-Element Solutions to Maxwell’s Equations ⋮ Near-field subsurface tomography and holography based on bistatic measurements with variable base ⋮ Inverse scattering reconstruction of a three dimensional sound-soft axis-symmetric impenetrable object ^* ⋮ Reconstruction of a local perturbation in inhomogeneous periodic layers from partial near field measurements ⋮ Left-handed lens tomography and holography ⋮ Inverse scattering problems of near-field subsurface pulse diagnostics ⋮ Numerical Scheme for Electromagnetic Scattering on Perturbed Periodic Inhomogeneous Media and Reconstruction of the Perturbation ⋮ A stabilized \(P1\) domain decomposition finite element method for time harmonic Maxwell's equations ⋮ High Resolution Inverse Scattering in Two Dimensions Using Recursive Linearization

Uses Software

• WavES

Cites Work

• Unnamed Item
• Unnamed Item
• Energy estimates and numerical verification of the stabilized domain decomposition finite element/Finite difference approach for time-dependent Maxwell's system
• Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem
• Synthesis of global convergence and adaptivity for a hyperbolic coefficient inverse problem in 3D
• Reconstruction of the Refractive Index from Experimental Backscattering Data Using a Globally Convergent Inverse Method
• Reconstruction of shapes and refractive indices from backscattering experimental data using the adaptivity
• A posteriori error estimates in a globally convergent FEM for a hyperbolic coefficient inverse problem
• Adaptive finite element method for a coefficient inverse problem for Maxwell's system
• Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems
• The philosophy of the approximate global convergence for multidimensional coefficient inverse problems
• Blind backscattering experimental data collected in the field and an approximately globally convergent inverse algorithm
• Medium induced resolution enhancement for broadband imaging
• A posteriori error estimates for the adaptivity technique for the Tikhonov functional and global convergence for a coefficient inverse problem
• Absorbing Boundary Conditions for the Numerical Simulation of Waves
• A POSTERIORI ERROR ESTIMATION IN COMPUTATIONAL INVERSE SCATTERING
• Reconstruction from blind experimental data for an inverse problem for a hyperbolic equation
• Relaxation property for the adaptivity for ill-posed problems
• Why a minimizer of the Tikhonov functional is closer to the exact solution than the first guess
• A new approximate mathematical model for global convergence for a coefficient inverse problem with backscattering data

This page was built for publication: Globally convergent and adaptive finite element methods in imaging of buried objects from experimental backscattering radar measurements