Inverse problem in optical tomography and its numerical investigation by iteratively regularized methods

DOI10.1515/156939405775199479zbMath1090.65146OpenAlexW4248922359MaRDI QIDQ5290367

Taufiquar Khan, Alexandra B. Smirnova, Anatoly B. Bakushinsky

Publication date: 28 April 2006

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

Full work available at URL: https://doi.org/10.1515/156939405775199479

zbMATH Keywords

convergenceregularizationLevenberg-Marquardt methodradiative transfer equationoptical tomographynonlinear least squares methoda posteriori stopping rulediffusion based inverse problemill-posed problem trust region method

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integro-partial differential equations (45K05) Biomedical imaging and signal processing (92C55) Inverse problems for integral equations (45Q05)

Related Items (8)

A globally accelerated numerical method for optical tomography with continuous wave source ⋮ Numerical solutions of the forward and inverse problems arising in diffuse optical tomography ⋮ Relative computational efficiency of iteratively regularized methods ⋮ A globally convergent numerical method for an inverse elliptic problem of optical tomography ⋮ Convergence results of a modified regularized gradient method for nonlinear ill-posed problems ⋮ A globally accelerated numerical method for optical tomography with continuous wave source ⋮ Numerical solution of a one-dimensional inverse problem by the discontinuous Galerkin method ⋮ A globally convergent numerical method for coefficient inverse problems for thermal tomography

Uses Software

• Matlab

Cites Work

• Unnamed Item
• Quasi-Newton approach to nonnegative image restorations
• An Algorithm for Least-Squares Estimation of Nonlinear Parameters
• An inverse Robin problem for Laplace's equation: theoretical results and numerical methods
• On convergence rates for the iteratively regularized Gauss-newton method
• Logarithmic convergence rates of the iteratively regularized Gauss - Newton method for an inverse potential and an inverse scattering problem
• ON APPLICATION OF GENERALIZED DISCREPANCY PRINCIPLE TO ITERATIVE METHODS FOR NONLINEAR ILL-POSED PROBLEMS
• Multiple Scattering in an Infinite Medium

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