On the identification of piecewise constant coefficients in optical diffusion tomography by level set
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.
Received: 15 May 2015
Revised: 14 December 2015
Accepted: 14 January 2016
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 L1 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.
Mathematics Subject Classification: 49N45 / 65N21 / 74J25
Key words: Optical tomography / parameter identification / level set regularization / numerical strategy
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