I. Akduman and R. Kress, Electrostatic imaging via conformal mapping, Inverse Problems, vol.18, issue.6, pp.1659-1672, 2002.
DOI : 10.1088/0266-5611/18/6/315

H. Ammari, J. Garnier, H. Kang, M. Lim, and S. Yu, Generalized polarization tensors for shape description, Numerische Mathematik, vol.70, issue.2, pp.199-224, 2014.
DOI : 10.1007/s00211-013-0561-5

URL : https://hal.archives-ouvertes.fr/hal-00933523

H. Ammari and H. Kang, Reconstruction of small inhomogeneities from boundary measurements [4] , Generalized polarization tensors, inverse conductivity problems, and dilute composite materials: a review, in Inverse problems, multi-scale analysis and effective medium theory, Polarization and moment tensors, pp.1-67, 2004.

L. Borcea, Electrical impedance tomography, Inverse Problems, vol.18, issue.6, pp.99-136, 2002.
DOI : 10.1088/0266-5611/18/6/201

L. Bourgeois and J. Dardé, A quasi-reversibility approach to solve the inverse obstacle problem, Inverse Problems and Imaging, vol.4, issue.3, pp.351-377, 2010.
DOI : 10.3934/ipi.2010.4.351

URL : https://hal.archives-ouvertes.fr/hal-00873059

L. Bourgeois and J. Dardé, The " exterior approach " to solve the inverse obstacle problem for the Stokes system, Inverse Probl. Imaging, vol.8, pp.23-51, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00937768

M. Brühl and M. Hanke, Numerical implementation of two noniterative methods for locating inclusions by impedance tomography, Inverse Problems, vol.16, issue.4, pp.1029-1042, 2000.
DOI : 10.1088/0266-5611/16/4/310

F. Cakoni and D. Colton, A qualitative approach to inverse scattering theory, Applied Mathematical Sciences, vol.188
DOI : 10.1007/978-1-4614-8827-9

F. Cakoni and R. Kress, Integral equation methods for the inverse obstacle problem with generalized impedance boundary condition, Inverse Problems, vol.29, issue.1, p.15005, 2013.
DOI : 10.1088/0266-5611/29/1/015005

A. Calderón, On an inverse boundary value problem, in Seminar on Numerical Analysis and its Applications to Continuum Physics, Soc. Brasil. Mat, pp.65-73, 1980.

Y. Capdeboscq, J. Fehrenbach, F. De-gournay, and O. Kavian, Imaging by Modification: Numerical Reconstruction of Local Conductivities from Corresponding Power Density Measurements, SIAM Journal on Imaging Sciences, vol.2, issue.4, pp.1003-1030, 2009.
DOI : 10.1137/080723521

D. Colton and A. Kirsch, A simple method for solving inverse scattering problems in the resonance region, Inverse Problems, vol.12, issue.4, pp.383-393, 1996.
DOI : 10.1088/0266-5611/12/4/003

D. Colton, M. Piana, and R. Potthast, A simple method using Morozov's discrepancy principle for solving inverse scattering problems, Inverse Problems, vol.13, issue.6, pp.1477-1493, 1997.
DOI : 10.1088/0266-5611/13/6/005

R. E. Curto and L. A. Fialkow, Recursiveness, positivity, and truncated moment problems, Houston J. Math, vol.17, pp.603-635, 1991.

P. J. Davis, Plane regions determined by complex moments, Journal of Approximation Theory, vol.19, issue.2, pp.148-153, 1977.
DOI : 10.1016/0021-9045(77)90037-5

URL : http://doi.org/10.1016/0021-9045(77)90037-5

P. Duren, Harmonic mappings in the plane, Cambridge Tracts in Mathematics, vol.156, 2004.
DOI : 10.1017/CBO9780511546600

K. Erhard and R. Potthast, A Numerical Study of the Probe Method, SIAM Journal on Scientific Computing, vol.28, issue.5, pp.1597-1612, 2006.
DOI : 10.1137/040607149

A. Friedman and M. Vogelius, Identification of small inhomogeneities of extreme conductivity by boundary measurements: a theorem on continuous dependence, Archive for Rational Mechanics and Analysis, vol.34, issue.4, pp.299-326, 1989.
DOI : 10.1007/BF00281494

G. H. Golub, P. Milanfar, and J. Varah, A Stable Numerical Method for Inverting Shape from Moments, SIAM Journal on Scientific Computing, vol.21, issue.4, pp.1222-1243, 1999.
DOI : 10.1137/S1064827597328315

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.160.5983

B. Gustafsson, C. He, P. Milanfar, and M. Putinar, Reconstructing planar domains from their moments, Inverse Problems, vol.16, issue.4, pp.1053-1070, 2000.
DOI : 10.1088/0266-5611/16/4/312

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.9120

B. Gustafsson, M. Putinar, E. B. Saff, and N. Stylianopoulos, Bergman polynomials on an archipelago: Estimates, zeros and shape reconstruction, Advances in Mathematics, vol.222, issue.4, pp.1405-1460, 2009.
DOI : 10.1016/j.aim.2009.06.010

URL : http://doi.org/10.1016/j.aim.2009.06.010

W. Hackbusch, Integral equations, International Series of Numerical Mathematics, vol.120, 1995.
DOI : 10.1007/978-3-0348-9215-5

H. Haddar and R. Kress, Conformal mappings and inverse boundary value problems, Inverse Problems, vol.21, issue.3, pp.935-953, 2005.
DOI : 10.1088/0266-5611/21/3/009

URL : https://hal.archives-ouvertes.fr/hal-00744137

H. Haddar and R. Kress, Conformal mapping and an inverse impedance boundary value problem, Journal of Inverse and Ill-posed Problems, vol.14, issue.8, pp.785-804, 2006.
DOI : 10.1515/156939406779768319

URL : https://hal.archives-ouvertes.fr/hal-00744029

H. Haddar and R. Kress, Conformal mapping and impedance tomography, Inverse Problems, vol.26, issue.7, pp.74002-74020, 2010.
DOI : 10.1088/0266-5611/26/7/074002

URL : https://hal.archives-ouvertes.fr/hal-00739325

M. Hanke and M. Brühl, Recent progress in electrical impedance tomography, Inverse Problems, vol.19, issue.6, pp.65-90, 2003.
DOI : 10.1088/0266-5611/19/6/055

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.8.321

M. Ikehata, Reconstruction of the shape of the inclusion by boundary measurements, Communications in Partial Differential Equations, vol.23, issue.7-8, pp.1459-1474, 1998.
DOI : 10.2307/2154460

M. Ikehata, Reconstruction of the support function for inclusion from boundary measurements, Journal of Inverse and Ill-posed Problems, vol.8, issue.4, pp.367-378, 2000.
DOI : 10.1515/jiip.2000.8.4.367

M. Ikehata and S. Siltanen, Numerical method for finding the convex hull of an inclusion in conductivity from boundary measurements, Inverse Problems, vol.16, issue.4, p.1043, 2000.
DOI : 10.1088/0266-5611/16/4/311

O. Ivanyshyn and R. Kress, Nonlinear Integral Equations for Solving Inverse Boundary Value Problems for Inclusions and Cracks, Journal of Integral Equations and Applications, vol.18, issue.1, pp.13-38, 2006.
DOI : 10.1216/jiea/1181075363

H. Kang, H. Lee, and M. Lim, Construction of conformal mappings by generalized polarization tensors, Mathematical Methods in the Applied Sciences, vol.41, issue.9, pp.1847-1854, 2015.
DOI : 10.1002/mma.3195

A. Kirsch, The factorization method for a class of inverse elliptic problems, Mathematische Nachrichten, vol.22, issue.3, pp.258-277, 2005.
DOI : 10.1002/mana.200310239

R. Kress, Inverse Dirichlet problem and conformal mapping, Mathematics and Computers in Simulation, vol.66, issue.4-5, pp.255-265, 2004.
DOI : 10.1016/j.matcom.2004.02.006

R. Kress, Inverse problems and conformal mapping, Complex Variables and Elliptic Equations, vol.2, issue.2-4, pp.301-316, 2012.
DOI : 10.1007/978-1-4612-0559-3

R. Kress and W. , Nonlinear integral equations and the iterative solution for an inverse boundary value problem, Inverse Problems, vol.21, issue.4, pp.1207-1223, 2005.
DOI : 10.1088/0266-5611/21/4/002

W. Mclean, Strongly elliptic systems and boundary integral equations, 2000.

P. Milanfar, M. Putinar, J. Varah, B. Gustafsson, and G. H. Golub, Shape reconstruction from moments: theory, algorithms, and applications, Proc. SPIE, Advanced Signal Processing Algorithms, Architectures, and Implementations X, pp.406-416, 2000.
DOI : 10.1117/12.406519

P. Milanfar, G. C. Verghese, W. C. Karl, and A. Willsky, Reconstructing polygons from moments with connections to array processing, Signal Processing, IEEE Transactions on, pp.43-432, 1995.
DOI : 10.1109/78.348126

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.17.6268

A. Munnier and K. Ramdani, Conformal mapping for cavity inverse problem: an explicit reconstruction formula, Applicable Analysis, vol.162, issue.1, pp.108-129, 2017.
DOI : 10.1016/j.aam.2004.12.002

URL : https://hal.archives-ouvertes.fr/hal-01196111

C. Pommerenke, Boundary behaviour of conformal maps, 1992.
DOI : 10.1007/978-3-662-02770-7

R. Potthast, A survey on sampling and probe methods for inverse problems, Inverse Problems, vol.22, issue.2, pp.1-47, 2006.
DOI : 10.1088/0266-5611/22/2/R01

M. Putinar, A two-dimensional moment problem, Journal of Functional Analysis, vol.80, issue.1, pp.1-8, 1988.
DOI : 10.1016/0022-1236(88)90060-2

URL : http://doi.org/10.1016/0022-1236(88)90060-2

O. Steinbach, Numerical approximation methods for elliptic boundary value problems, 2008.
DOI : 10.1007/978-0-387-68805-3

G. Wen, Conformal Mappings and Boundary Value Problems, Translations of Mathematical Monographs, vol.106, 1992.