Carpio Rodríguez, Ana María and Rapún, M.L.
(2010)
*An iterative method for parameter identification and shape reconstruction.*
Inverse Problems in Science and Engineering, 18
(1).
pp. 35-50.
ISSN 1741-5977

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## Abstract

An iterative strategy for the reconstruction of objects buried in a medium and the identification of their material parameters is analysed. The algorithm alternates guesses of the domains using topological derivatives with corrections of the parameters obtained by descent techniques. Numerical experiments in geometries with multiple scatterers show that our scheme predicts the number, location and shape of objects, together with their physical parameters, with reasonable accuracy in a few steps.

Item Type: | Article |
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Uncontrolled Keywords: | Inverse scattering; topological derivative; domain reconstruction; parameter identification; non-destructive testing; scattering; inverse transmission problems |

Subjects: | Sciences > Physics > Electromagnetism Sciences > Mathematics > Differential equations |

ID Code: | 14888 |

References: | [1] M. Bonnet and A. Constantinescu, Inverse problems in elasticity, Inverse Probl. 21 (2005), pp. R1–R50. [2] G.R. Feijoo, A new method in inverse scattering based on the topological derivative, Inverse Probl. 20 (2004), pp. 1819–1840. [3] B.B. Guzina and M. Bonnet, Small-inclusion asymptotic of misfit functionals for inverse problems in acoustics, Inverse Probl. 22 (2006), pp. 1761–1785. [4] A. Carpio and M.L. Rapu´ n, Solving inverse inhomogeneous problems by topological derivative methods, Inverse Probl. 24 (2008), p. 045014. [5] B.B. Guzina and I. Chikichev, From imaging to material identification: A generalized concept of topological sensitivity, J. Mech. Phys. Solids 55 (2007), pp. 245–279. [6] B. Delattre, D. Ivaldi, and C. Stolz, Application du controˆle optimal a` l’identification d’un chargement thermique, Rev. Eur. Elem. Finites 11 (2002), pp. 393–404. [7] A. Peters, H.U. Berger, J. Chase, and E. Van Houten, Digital-image based elasto-tomography: Nonlinear mechanical property reconstruction of homogeneous gelatine phantoms, Int. J. Inf. Syst. Sci. 2 (2006), pp. 512–521. [8] K.D. Paulsen, P.M. Meaney, and L. Gilman, Alternative Breast Imaging: Four Model Based Approaches, Springer Series in Engineering and Computer Science, Vol. 778, Springer, Boston, 2005. [9] Q.H. Liu, Z.Q. Zhang, T.T. Wang, J.A. Bryan, G.A. Ybarra, L.W. Nolte, and W.T. Joines, Active microimaging I-2-D forward and inverse scattering methods, IEEE Trans. Micr. Theor. Tech. 50 (2002), pp. 123–133. [10] H.T. Liu, L.Z. Sun, G. Wang, and M.W. Vannier, Analytic modeling of breast elastography, Med. Phys. 30 (2003), pp. 2340–2349. [11] A. Carpio and M.L. Rapu´ n, Domain reconstruction by photothermal techniques, J. Comput. Phys. 227 (2008), pp. 8083–8106. [12] F. Santosa, A level set approach for inverse problems involving obstacles, ESAIM Control, Optim. Calculus Variations 1 (1996), pp. 17–33. [13] A. Carpio and M.L. Rapu´ n, Topological Derivatives for Shape Reconstruction, Lecture Notes in Mathematics, Vol. 1943, Springer, Berlin, 2008, pp. 85–131. [14] A. Carpio and M.L. Rapu´ n, Topological derivative based methods for non-destructive testing, in Numerical Mathematics and Advanced Applications, K. Kunisch, G. Of, and O. Steinbach,eds., Springer, Berlin, 2008, pp. 687–694. [15] M.L. Rapu´ n and F.J. Sayas, A mixed-FEM and BEM coupling for the approximation of the scattering of thermal waves in locally non-homogeneous media, ESAIM Math. Model. Numer. Anal. 40 (2006), pp. 871–896. [16] O. Dorn and D. Lesselier, Level set methods for inverse scattering, Inverse Probl. 22 (2006), pp. R67–R131. [17] A. Litman, D. Leselier, and F. Santosa, Reconstruction of a two-dimensional binary obstacle by controlled evolution of a level-set, Inverse Probl. 14 (1998), pp. 68–706. [18] M.L. Rapu´ n and F.J. Sayas, Indirect methods with Brakhage–Werner potentials for Helmholtz transmission problems, in Numerical Mathematics and Advanced Applications, A. Bermu´ dez de Castro, D. Go´ mez, P. Quintela, and P. Salgado, eds., Springer, Berlin, 2006, pp. 1146–1154. |

Deposited On: | 19 Apr 2012 08:57 |

Last Modified: | 06 Feb 2014 10:11 |

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