Optical tomography reconstruction algorithm with the finite element method: An optimal approach with regularization tools
- LTN UMR CNRS 6607 – Polytech’ Nantes – La Chantrerie, Rue Christian Pauc, BP 50609 44 306 Nantes Cedex 3 (France)
- Chaire de recherche industrielle en technologies de l’énergie et en efficacité énergétique (t3e), École de technologie supérieure, 201 Boul. Mgr, Bourget Lévis, QC, Canada G6V 6Z3 (Canada)
Highlights: •New strategies to improve the accuracy of the reconstruction through mesh and finite element parameterization. •Use of gradient filtering through an alternative inner product within the adjoint method. •An integral form of the cost function is used to make the reconstruction compatible with all finite element formulations, continuous and discontinuous. •Gradient-based algorithm with the adjoint method is used for the reconstruction. -- 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.
- OSTI ID:
- 22230813
- Journal Information:
- Journal of Computational Physics, Vol. 251; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
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