Geodesic
On the identification of piecewise constant coefficients in optical diffusion tomography by level set
Agnelli, J. P.1 ; De Cezaro, A.2 ; Leitão, A.3 ; Marques Alves, M.3
1 FaMAF-CIEM (CONICET), Universidad Nacional de Córdoba, Medina Allende s/n, X5000HUA, Córdoba, Argentina.
2 Institute of Mathematics Statistics and Physics, Federal University of Rio Grande, Av. Italia km 8, 96201-900 Rio Grande, Brazil.
3 Department of Mathematics, Federal University of St. Catarina, P.O. Box 476, 88040-900 Florianópolis, Brazil.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 2, pp. 663-683

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In this paper, we propose a level set regularization approach combined with a split strategy for the simultaneous identification of piecewise constant diffusion and absorption coefficients from a finite set of optical tomography data (Neumann-to-Dirichlet data). This problem is a high nonlinear inverse problem combining together the exponential and mildly ill-posedness of diffusion and absorption coefficients, respectively. We prove that the parameter-to-measurement map satisfies sufficient conditions (continuity in the L 1 topology) to guarantee regularization properties of the proposed level set approach. On the other hand, numerical tests considering different configurations bring new ideas on how to propose a convergent split strategy for the simultaneous identification of the coefficients. The behavior and performance of the proposed numerical strategy is illustrated with some numerical examples.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2016007
Classification : 49N45, 65N21, 74J25
Keywords: Optical tomography, parameter identification, level set regularization, numerical strategy

Agnelli, J. P. 1 ; De Cezaro, A. 2 ; Leitão, A. 3 ; Marques Alves, M. 3

1 FaMAF-CIEM (CONICET), Universidad Nacional de Córdoba, Medina Allende s/n, X5000HUA, Córdoba, Argentina.
2 Institute of Mathematics Statistics and Physics, Federal University of Rio Grande, Av. Italia km 8, 96201-900 Rio Grande, Brazil.
3 Department of Mathematics, Federal University of St. Catarina, P.O. Box 476, 88040-900 Florianópolis, Brazil. 
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     title = {On the identification of piecewise constant coefficients in optical diffusion tomography by level set},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {663--683},
     publisher = {EDP-Sciences},
     volume = {23},
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Agnelli, J. P.; De Cezaro, A.; Leitão, A.; Marques Alves, M. On the identification of piecewise constant coefficients in optical diffusion tomography by level set. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 2, pp. 663-683. doi: 10.1051/cocv/2016007

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