A wavelet multi-scale method for the inverse problem of diffuse optical tomography

DOI10.1016/j.cam.2015.01.023zbMath1317.65194OpenAlexW1979170794MaRDI QIDQ2352315

D. R. Rousse, B. Rousseau, F. Dubot, Yann Favennec

Publication date: 30 June 2015

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

Full work available at URL: https://doi.org/10.1016/j.cam.2015.01.023

zbMATH Keywords

convergenceinversionnumerical resultnonlinear ill-posed inverse problemoptical tomographyoptical propertiesBroyden-Fletcher-Goldfarb-Shanno (BFGS) methodL-BFGS algorithmwavelet multi-scale method

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Ill-posed problems for PDEs (35R25) Inverse problems for PDEs (35R30) Numerical methods for wavelets (65T60) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32)

Related Items (10)

Modeling the one-dimensional inverse heat transfer problem using a Haar wavelet collocation approach ⋮ A wavelet multiscale method for the inverse problem of a nonlinear convection-diffusion equation ⋮ Specular reflection treatment for the 3D radiative transfer equation solved with the discrete ordinates method ⋮ Wavelet-based priors accelerate maximum-a-posteriori optimization in Bayesian inverse problems ⋮ Reconstruction of a permeability field with the wavelet multiscale-homotopy method for a nonlinear convection-diffusion equation ⋮ Estimation of a permeability field within the two-phase porous media flow using nonlinear multigrid method ⋮ A wavelet multiscale-homotopy method for the parameter identification problem of partial differential equations ⋮ Space-dependent Sobolev gradients as a regularization for inverse radiative transfer problems ⋮ Reactive fluid flow topology optimization with the multi-relaxation time lattice Boltzmann method and a level-set function ⋮ A wavelet multi-scale method for the inverse problem of diffuse optical tomography

Uses Software

• FreeFem++
• L-BFGS

Cites Work

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