article

Optical tomography reconstruction algorithm with the finite element method: An optimal approach with regularization tools

Authors:

D. RousseAuthors Info & Claims

Journal of Computational Physics, Volume 251

Pages 461 - 479

https://doi.org/10.1016/j.jcp.2013.04.043

Published: 01 October 2013 Publication History

Abstract

Optical tomography is mathematically treated as a non-linear inverse problem where the optical properties of the probed medium are recovered through the minimization of the errors between the experimental measurements and their predictions with a numerical model at the locations of the detectors. According to the ill-posed behavior of the inverse problem, some regularization tools must be performed and the Tikhonov penalization type is the most commonly used in optical tomography applications. This paper introduces an optimized approach for optical tomography reconstruction with the finite element method. An integral form of the cost function is used to take into account the surfaces of the detectors and make the reconstruction compatible with all finite element formulations, continuous and discontinuous. Through a gradient-based algorithm where the adjoint method is used to compute the gradient of the cost function, an alternative inner product is employed for preconditioning the reconstruction algorithm. Moreover, appropriate re-parameterization of the optical properties is performed. These regularization strategies are compared with the classical Tikhonov penalization one. It is shown that both the re-parameterization and the use of the Sobolev cost function gradient are efficient for solving such an ill-posed inverse problem.

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Cited By

Dugast FFavennec YJosset CFan YLuo L(2018)Topology optimization of thermal fluid flows with an adjoint Lattice Boltzmann MethodJournal of Computational Physics10.1016/j.jcp.2018.03.040365:C(376-404)Online publication date: 15-Jul-2018
https://dl.acm.org/doi/10.1016/j.jcp.2018.03.040
Dubot FFavennec YRousseau BRousse D(2015)A wavelet multi-scale method for the inverse problem of diffuse optical tomographyJournal of Computational and Applied Mathematics10.1016/j.cam.2015.01.023289:C(267-281)Online publication date: 1-Dec-2015
https://dl.acm.org/doi/10.1016/j.cam.2015.01.023

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cover image Journal of Computational Physics

Journal of Computational Physics Volume 251, Issue

October, 2013

534 pages

ISSN:0021-9991

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Copyright © © 2013.

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Academic Press Professional, Inc.

United States

Publication History

Published: 01 October 2013

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Cited By

Dugast FFavennec YJosset CFan YLuo L(2018)Topology optimization of thermal fluid flows with an adjoint Lattice Boltzmann MethodJournal of Computational Physics10.1016/j.jcp.2018.03.040365:C(376-404)Online publication date: 15-Jul-2018
https://dl.acm.org/doi/10.1016/j.jcp.2018.03.040
Dubot FFavennec YRousseau BRousse D(2015)A wavelet multi-scale method for the inverse problem of diffuse optical tomographyJournal of Computational and Applied Mathematics10.1016/j.cam.2015.01.023289:C(267-281)Online publication date: 1-Dec-2015
https://dl.acm.org/doi/10.1016/j.cam.2015.01.023

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