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Parameter Identification in Photothermal Imaging

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Abstract

We propose a technique to reconstruct the geometry of inclusions and their material parameters in thermal scattering near surfaces. The imaging problem is reformulated as a constrained optimization problem with a finite number of stationary constraints. The unknown domains and their parameters are the design variables. A descent method combining topological derivative analysis to find improved guesses of the objects and gradient iterations to correct their material parameters provides reasonable reconstructions.

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Acknowledgements

The authors are partially supported by the Spanish Government research project TRA2010–18054 and the Spanish Ministerio de Economia y Competitividad Grants No. FIS2011-28838-C02-02, and No. FIS2010-22438-E.

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Authors and Affiliations

  1. Dept. Matemática Aplicada, Universidad Complutense de Madrid, Madrid, Spain

    A. Carpio

  2. Dept. Fundamentos Matemáticos, ETSI Aeronáuticos, Universidad Politécnica de Madrid, Madrid, Spain

    M.-L. Rapún

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  1. A. Carpio
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  2. M.-L. Rapún
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Correspondence to M.-L. Rapún.

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Carpio, A., Rapún, ML. Parameter Identification in Photothermal Imaging. J Math Imaging Vis 49, 273–288 (2014). https://doi.org/10.1007/s10851-013-0459-y

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