1D inverse problem in diffusion based optical tomography using iteratively regularized Gauss--Newton algorithm

DOI10.1016/j.amc.2003.12.019zbMath1061.65142OpenAlexW2159329733MaRDI QIDQ1763229

Xianqiang Yang

Publication date: 22 February 2005

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

Full work available at URL: https://doi.org/10.1016/j.amc.2003.12.019

zbMATH Keywords

numerical examplesiterative regularizationnonlinear ill-posed problemInverse problemsoptical tomographyArmijo-Goldstein-Wolf type line search strategyBiomedical imagingIteratively regularized Gauss-Newton methodReconstruction algorithms

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)

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Investigation of a non-iterative technique based on topological derivatives for fast localization of small conductivity inclusions ⋮ An Optimal Bayesian Estimator for Absorption Coefficient in Diffuse Optical Tomography ⋮ Direct sampling method for identifying magnetic inhomogeneities in limited-aperture inverse scattering problem ⋮ Convergence results of a modified regularized gradient method for nonlinear ill-posed problems ⋮ Some convergence results of a modified asymptotical regularization gradient method for nonlinear ill-posed operator equation ⋮ Comparison of statistical inversion with iteratively regularized Gauss Newton method for image reconstruction in electrical impedance tomography ⋮ Numerical solution of a one-dimensional inverse problem by the discontinuous Galerkin method ⋮ Inverse Problems Involving PDEs with Applications to Imaging

Cites Work

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• Quasi-Newton approach to nonnegative image restorations
• Mathematical Methods in Image Reconstruction
• An Algorithm for Least-Squares Estimation of Nonlinear Parameters
• Optical tomography in medical imaging
• Numerical Solution of a Parabolic Inverse Problem in Optical Tomography Using Experimental Data
• 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
• Multiple Scattering in an Infinite Medium
• A method for the solution of certain non-linear problems in least squares

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