Relative computational efficiency of iteratively regularized methods

DOI10.1515/JIIP.2008.041zbMath1155.65041OpenAlexW2056671357MaRDI QIDQ3548643

Necibe Tuncer, Anatoly B. Bakushinsky, Alexandra B. Smirnova

Publication date: 16 December 2008

Published in: Journal of Inverse and Ill-posed Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jiip.2008.041

zbMATH Keywords

inverse problemregularizationnumerical examplesHilbert spacenonlinear operator equationGauss-Newton methodradiative transport equationoptical tomographyFréchet and Gâteaux derivativesill-posed optical tomography inverse problem

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Biomedical imaging and signal processing (92C55) Nonlinear ill-posed problems (47J06) Numerical solutions to equations with nonlinear operators (65J15) Complexity and performance of numerical algorithms (65Y20) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)

Uses Software

• DistMesh

Cites Work

• A modified Landweber iteration for solving parameter estimation problems
• Optical tomography in medical imaging
• Inverse problem in optical tomography and its numerical investigation by iteratively regularized methods
• Inverse problem in refractive index based optical tomography
• Convergence and application of a modified iteratively regularized Gauss–Newton algorithm

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