Sampling method based projection approach for the reconstruction of 3D acoustically penetrable scatterers

DOI10.1016/j.laa.2015.12.020zbMath1333.65124OpenAlexW2254511423MaRDI QIDQ5962849

Andreas Kleefeld, Koung Hee Leem, George Pelekanos, Fermin S. Viloche Bazán

Publication date: 24 February 2016

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2015.12.020

zbMATH Keywords

numerical exampleinverse problemregularizationacoustic scatteringHelmholtz equationfactorization methodfar-field matrixgeneralized discrepancy principleGolub-Kahan bidiagonalization algorithmLanczos tridiagonalization processlinear sampling method

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Inverse problems for PDEs (35R30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary element methods for boundary value problems involving PDEs (65N38) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)

Related Items

Two direct factorization methods for inverse scattering problems ⋮ Detecting and approximating decision boundaries in low-dimensional spaces ⋮ A numerical reconstruction method in inverse elastic scattering ⋮ A numerical comparison of different qualitative algorithms for solving 2D inverse elastic scattering problems

Uses Software

• LSQR
• Regularization tools
• GKB-FP
• mftoolbox
• CRAIG

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A maximum product criterion as a Tikhonov parameter choice rule for Kirsch's factorization method
• On the generalized discrepancy principle for Tikhonov regularization in Hilbert scales
• Fixed-point iterations in determining a Tikhonov regularization parameter in Kirsch's factorization method
• A direct boundary integral equation method for transmission problems
• A bidiagonalization algorithm for solving large and sparse ill-posed systems of linear equations
• Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems
• GKB-FP: An algorithm for large-scale discrete ill-posed problems
• Simple and efficient determination of the Tikhonov regularization parameter chosen by the generalized discrepancy principle for discrete ill-posed problems
• Using the linear sampling method and an improved maximum product criterion for the solution of the electromagnetic inverse medium problem
• SVD-tail: a new linear-sampling reconstruction method for inverse scattering problems
• Shape reconstruction of a 2D-elastic penetrable object via the L-curve method
• Fixed-point iterations in determining the Tikhonov regularization parameter
• Regularization of linear ill-posed problems with noisy right hand side and noisy operator
• On Single Integral Equations for the Transmission Problem of Acoustics
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• Characterization of the shape of a scattering obstacle using the spectral data of the far field operator
• A simple method using Morozov's discrepancy principle for solving inverse scattering problems
• The linear sampling method in inverse electromagnetic scattering theory
• The linear sampling method for solving the electromagnetic inverse medium problem
• Uniqueness in inverse obstacle scattering (acoustics)
• A simple method for solving inverse scattering problems in the resonance region
• The Linear Sampling Method for Solving the Electromagnetic Inverse Scattering Problem
• The factorization method for the acoustic transmission problem
• Functions of Matrices
• Extension of GKB‐FP algorithm to large‐scale general‐form Tikhonov regularization
• Inverse acoustic and electromagnetic scattering theory