A. Kirsch, An introduction to the Mathematical Theory of Inverse Problems, Applied Mathematical Sciences, vol.120, 1996.

A. B. Abda, J. Henry, and F. Jday, Boundary data completion: The method of boundary value problem factorization, Inverse Problems, vol.27, issue.5, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00617511

V. Albani, P. Elbau, M. V. De-hoop, and O. Scherzer, Optimal convergence rates results for linear inverse problems in hilbert spaces, Numerical Functional Analysis and Optimization, vol.37, issue.5, pp.521-540, 2016.

A. M. Denisov, Elements of the Theory of Inverse Problems, 2014.

N. Aronszajn, A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order, J. Math. Pures Appl, 1957.

M. Azaez, H. E. Faker-ben-belgacem, and . Fekih, On cauchy's problem: Ii. completion, regularization and approximation, Inverse Problems, vol.22, issue.4, p.1307, 2006.

. Faker-ben-belgacem, Why is the cauchy problem severely ill-posed? Inverse Problems, vol.23, p.823, 2007.

B. Faker, H. E. Belgacem, and . Fekih, On cauchy's problem: I. a variational steklov?poincaré theory, Inverse Problems, vol.21, issue.6, p.1915, 2005.

N. Bouarroudj, J. Henry, B. Louro, and M. Orey, On a direct study of an operator riccati equation appearing in boundary value problems factorization. Applied mathematical sciences, vol.46, pp.2247-2257, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00387563

J. Bouyssier, N. Zemzemi, and J. Henry, Inverse problem in electrocardography via the factorization method of boundary value problems, pp.743-746, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01222401

M. Burger and S. Osher, Convergence rates of convex variational regularization. Inverse Problems, vol.20, pp.1411-1421, 2004.

J. Chamorro-servent, R. Dubois, M. Potse, and Y. Ere, Improving the spatial solution of electrocardiographic imaging: A new regularization parameter choice technique for the tikhonov method, Functional Imaging and Modelling of the Heart, pp.289-300, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01564899

M. J. Cluitmans, R. L. Peeters, R. L. Westra, and P. G. Volders, Noninvasive reconstruction of cardiac electrical activity: Update on current methods, applications and challenges, Netherlands Heart Journal, vol.23, issue.6, pp.301-311, 2015.

S. Sergei, G. , G. Anna, and V. , On the a posteriori choice of a regularization parameter in the solution of severely ill-posed problems, Journal of Mathematical Sciences, vol.181, issue.1, pp.98-105, 2012.

P. C. Hansen, Regularization tools: A matlab package for analysis and solution of discrete ill-posed problems, Numerical Algorithms, vol.6, issue.1, pp.1-35, 1994.

J. Henry and A. M. Ramos, Factorization of Boundary Value Problems Using the Invariant Embedding Method, pp.1-238, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01413582

J. Hadamard, Lecture The Cauchy problem in linear partial differential equations, 1923.

J. L. Lions and E. Magenes, Non-Homogeneous Bondary Value Problems and Applications, vol.1, 1972.

T. Luc, An Introduction to Sobolev Spaces and Interpolation Spaces, 2007.

D. G. Luenberger, Optimization by Vector Spaces Methods, 1969.

E. Resmerita, Regularization of ill-posed problems in banach spaces: Convergence rates, Inverse Problems, vol.21, issue.4, pp.1303-1314, 2005.

S. G. Solodky, Morozov's discrepancy principle for the tikhonov regularization of exponentially ill-posed problems, Computational Methods in Applied Mathematics, vol.8, issue.1, pp.86-98, 2008.

S. G. Solodky and G. L. Myleiko, On optimization of projection methods for solving some classes of severely ill-posed problems, Applicable Analysis, vol.95, issue.4, pp.826-841, 2016.

U. Tautenhahn, Optimality for ill-posed problems under general source conditions. Numerical Functional Analysis and Optimization, vol.19, pp.377-398, 1998.

H. Thorsten, Regularization of exponentially ill-posed problems, Numer. Funct. Anal. and Optimiz, vol.21, pp.439-464, 2000.

V. Isakov, Inverse Problems for Partial Differential Equations, 1998.

V. P. Mijailov, Ecuaciones Diferenciales en Derivadas Parciales. Moscu, 1978.

T. Wei and Y. G. Chen, A regularization method for a cauchy problem of laplace's equation in an annular domain, Mathematics and Computers in Simulation, vol.82, issue.11, pp.2129-2144, 2012.