New developments in frequency domain optical tomography. Part I: Forward model and gradient computation |
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Authors: | O Balima J Boulanger D Marceau |
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Institution: | a Groupe de Recherche en Ingénierie des Procédés et Systèmes, Université du Québec à Chicoutimi, Que., Canada G7H 2B1 b National Research Council, Montreal Rd Campus. M-10, Ottawa, Ont., Canada K1A 0R6 |
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Abstract: | This two part study introduces new developments in frequency domain optical tomography to take into account the collimated source direction in the computation of both the forward and the adjoint models. The solution method is based on the least square finite element method associated to the discrete ordinates method where no empirical stabilization is needed. In this first part of the study, the solution method of the forward model is highlighted with an easy handling of complex boundary condition through a penalization method. Gradient computation from an adjoint method is developed rigorously in a continuous manner through a lagrangian formalism for the deduction of the adjoint equation and the gradient of the objective function. The proposed formulation can be easily generalized to stationary and time domain optical tomography by keeping the same expressions. |
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Keywords: | Radiative transfer equation Frequency domain Finite elements Discrete ordinates Adjoint method Lagrangian formulation |
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