References
- A. Altundag and R. Kress. On a two-dimensional inverse scattering problem for a dielectric. Applicable Analysis, 91(4):757–771, 2012. https://doi.org/10.1080/00036811.2011.619981.
- H. Ammari, E. Bonnetier, Y. Capdeboscq, M. Tanter and M. Fink. Electrical impedance tomography by elastic deformation. SIAM Journal on Applied Mathematics, 68(6):1557–1573, 2008. https://doi.org/10.1137/070686408.
- K. Astala and L. Päivärinta. Calderón’s inverse conductivity problem in the plane. Annals of Mathematics, 126(1):265–299, 2006. https://doi.org/10.4007/annals.2006.163.265.
- X. Bai and B. He. Estimation of number of independent brain electric sources from the scalp EEGs. IEEE transactions on bio-medical engineering, 53(10):1883–1892, 2006. https://doi.org/10.1109/TBME.2006.876620.
- A.L. Bukhgeim. Recovering a potential from Cauchy data in the twodimensional case. Journal of Inverse and Ill-posed Problems, 16(1):19–33, 2008. https://doi.org/10.1515/jiip.2008.002.
- M. Cheney, D. Isaacson and J.C. Newell. Electrical impedance tomography. Industrial Tomography, 41(1):23–59, 2002.
- T.F. Coleman and Y. Li. On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds. Mathematical programming, 67(1):189–224, 1994. https://doi.org/10.1007/BF01582221.
- T.F. Coleman and Y. Li. An interior, trust region approach for nonlinear minimization subject to bounds. SIAM Journal on Optimization,, 6(2):418–445, 1996. https://doi.org/10.1137/0806023.
- R. Duraiswami, G.L. Chahine and K. Sarkar. Boundary element techniques for efficient 2-D and 3-D electrical impedance tomography. Chemical engineering science, 52(13):2185–2196, 1997. https://doi.org/10.1016/S0009-2509(97)00044-4.
- H. Eckel and R. Kress. Nonlinear integral equations for the inverse electrical impedance problem. Inverse Problems, 23(2):475, 2007. https://doi.org/10.1088/0266-5611/23/2/002.
- W. Fang and E. Cumberbatch. Inverse problems for metal oxide semiconductor field-effect transistor contact resistivity. SIAM Journal on Applied Mathematics, 52(3):699–709, 1992. https://doi.org/10.1137/0152039.
- B. Gebauer and N. Hyvönen. Factorization method and irregular inclusions in electrical impedance tomography. Inverse Problems, 23(5):2159, 2007. https://doi.org/10.1088/0266-5611/23/5/020.
- H.G. Gene, M.T. Heath and G. Wahba. Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter. Technometrics, 21(2):215–223, 1979. https://doi.org/10.1080/00401706.1979.10489751.
- B. Haberman and D. Tataru. Uniqueness in Calderón’s problem with Lipschitz conductivities. Duke Mathematical Journal, 162(3):497–516, 2013. https://doi.org/10.1215/00127094-2019591.
- P.C. Hansen. Rank-deficient and Discrete Ill-posed Problems: Numerical Aspects of Linear Inversion. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 1998. ISBN 0-89871-403-6. https://doi.org/10.1137/1.9780898719697.
- O.Y. Imanuvilov and M. Yamamoto. Inverse boundary value problem for Schrödinger equation in two dimensions. SIAM Journal on Mathematical Analysis, 44(3):1333–1339, 2012. https://doi.org/10.1137/11083736X.
- O.Y. Imanuvilov and M. Yamamoto. Inverse boundary value problem for the Schrödinger equation in a cylindrical domain by partial boundary data. Inverse Problems, 29(4):045002, 2013. https://doi.org/10.1088/0266- 5611/29/4/045002.
- H. Kang. A uniqueness theorem for an inverse boundary value problem in two dimensions. Journal of mathematical analysis and applications, 270(1):291–302, 2002. https://doi.org/10.1016/S0022-247X(02)00085-9.
- R. Kohn and M. Vogelius. Determining conductivity by boundary measurements. Communications on Pure and Applied Mathematics, 38(3):289–298, 1984. https://doi.org/10.1002/cpa.3160370302.
- R. Kohn and M. Vogelius. Determining conductivity by boundary measurements II. Interior results. Communications on Pure and Applied Mathematics, 38(5):643–667, 1985.
- R. Kress. Linear integral equations, volume 82 of Applied Mathematical Sciences. Springer-Verlag, New York, second edition, 1999. https://doi.org/10.1007/978-1-4612-0559-3.
- R. Kress and W. Rundell. Nonlinear integral equations and the iterative solution for an inverse boundary value problem. Inverse Problems, 21(4):1207, 2005. https://doi.org/10.1088/0266-5611/21/4/002.
- D.G. Luenberger. Introduction to linear and nonlinear programming, volume 28. Addison-Wesley Reading, MA, 1973.
- D.W. Marquardt. An algorithm for least-squares estimation of nonlinear parameters. Journal of the Society for Industrial & Applied Mathematics, 11(2):431–441, 1963. https://doi.org/10.1137/0111030.
- V. Morozov. Methods of Solving Incorrectly Posed Problems. Springer-Verlag, New York, 1984. https://doi.org/10.1007/978-1-4612-5280-1.
- A. Nachman. Reconstructions from boundary measurements. Ann. of Math., 128(3):531–576, 1988. https://doi.org/10.2307/1971435.
- A.I. Nachman. Global uniqueness for a two-dimensional inverse boundary value problem. Annals of Mathematics, 143(1):71–96, 1996. https://doi.org/10.2307/2118653.
- G. Nakamura, Z. Sun and G. Uhlmann. Global identifiability for an inverse problem for the Schrödinger equation in a magnetic field. Mathematische Annalen, 303(1):377–388, 1995. https://doi.org/10.1007/BF01460996.
- H.H. Qin and F. Cakoni. Nonlinear integral equations for shape reconstruction in the inverse interior scattering problem. Inverse Problems, 27(3):563–648, 2011. https://doi.org/10.1088/0266-5611/27/3/035005.
- A.G. Ramm. A uniqueness theorem for a boundary inverse problem. Inverse Problems, 4(1):L1, 1988. https://doi.org/10.1088/0266-5611/4/1/001.
- J. Sylvester and G. Uhlmann. A global uniqueness theorem for an inverse boundary value problem. Annals of mathematics, 125(1):153–169, 1987. https://doi.org/10.2307/1971291.
- J. Sylvester and G. Uhlmann. Inverse boundary value problems at the boundarycontinuous dependence. Communications on pure and applied mathematics, 41(2):197–219, 1988. https://doi.org/10.1002/cpa.3160410205.