Publication: An iterative method for parameter identification and shape reconstruction
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2010
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Taylor & Francis
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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.
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[1] M. Bonnet and A. Constantinescu, Inverse problems in elasticity, Inverse Probl. 21 (2005),
pp. R1âR50.
[2] G.R. Feijoo, A new method in inverse scattering based on the topological derivative, Inverse Probl.
20 (2004), pp. 1819â1840.
[3] B.B. Guzina and M. Bonnet, Small-inclusion asymptotic of misfit functionals for inverse problems
in acoustics, Inverse Probl. 22 (2006), pp. 1761â1785.
[4] A. Carpio and M.L. RapuÂŽ 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. 245â279.
[6] B. Delattre, D. Ivaldi, and C. Stolz, Application du controËle optimal a` lâidentification dâun
chargement thermique, Rev. Eur. Elem. Finites 11 (2002), pp. 393â404.
[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. 512â521.
[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. 123â133.
[10] H.T. Liu, L.Z. Sun, G. Wang, and M.W. Vannier, Analytic modeling of breast elastography,
Med. Phys. 30 (2003), pp. 2340â2349.
[11] A. Carpio and M.L. RapuÂŽ n, Domain reconstruction by photothermal techniques, J. Comput.
Phys. 227 (2008), pp. 8083â8106.
[12] F. Santosa, A level set approach for inverse problems involving obstacles, ESAIM Control, Optim.
Calculus Variations 1 (1996), pp. 17â33.
[13] A. Carpio and M.L. RapuÂŽ n, Topological Derivatives for Shape Reconstruction, Lecture Notes in
Mathematics, Vol. 1943, Springer, Berlin, 2008, pp. 85â131.
[14] A. Carpio and M.L. RapuÂŽ 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. 687â694.
[15] M.L. RapuÂŽ 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. 871â896.
[16] O. Dorn and D. Lesselier, Level set methods for inverse scattering, Inverse Probl. 22 (2006),
pp. R67âR131.
[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. 68â706.
[18] M.L. RapuÂŽ n and F.J. Sayas, Indirect methods with BrakhageâWerner potentials for Helmholtz
transmission problems, in Numerical Mathematics and Advanced Applications, A. BermuÂŽ dez de
Castro, D. GoÂŽ mez, P. Quintela, and P. Salgado, eds., Springer, Berlin, 2006, pp. 1146â1154.