R. Aboulaich, A. B. Abda, and M. , Kallel, missing boundary data reconstruction via an approximate optimal control, Inverse Problems and Imaging, vol.2, issue.4, pp.411-426, 2008.

R. Aboulaich, N. Fikal, E. E. Guarmah, and N. Zemzemi, Stochastic finite element method for torso conductivity uncertainties quantification in electrocardiography inverse problem, Mathematical Modelling of Natural Phenomena, vol.11, issue.2, pp.1-19, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01289144

S. Andrieux, T. Baranger, and A. B. Abda, Solving cauchy problems by minimizing an energy-like functional, Inverse problems, vol.22, issue.1, pp.115-133, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00139569

V. Asokan, B. Narayanan, and N. Zabaras, Stochastic inverse heat conduction using a spectral approach, Int. J. Numer. Meth. Engng, vol.60, issue.7, pp.1-24, 2004.

I. Babuska, R. Tempone, and G. Zouraris, Galerkin finite element approximations of stochastic elliptic partial differential equations, SIAM Journal on Numerical Analysis, vol.42, issue.2, pp.800-825, 2005.

I. Babuska, R. Tempone, and G. Zouraris, Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation, Comput. Methods Appl. Mech. Engrg, vol.194, pp.1251-1294, 2005.

J. Barbara and Y. Rudy, The inverse problem in electrocardiography: A model study of the effects of geometry and conductivity parameters on the reconstruction of epicardial potentials, IEEE transactions on biomedical engineering, vol.33, issue.7, pp.667-676, 1986.

M. Berveiller, Eléments finis stochastiques: approches intrusive et non intrusive pour des analyses de fiabilité, 2005.

M. Boulakia, C. Serge, M. Fernández, G. Jean-frédéric, and N. Zemzemi, Mathematical modeling of electrocardiograms: a numerical study, Annals of biomedical engineering, vol.38, issue.3, pp.1071-1097, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00400490

C. Bullard and A. Sebald, Monte carlo sensitivity analysis of input-output models, The Review of Economics and Statistics, vol.70, issue.1, pp.708-712, 1988.

Y. Cao, M. Hussaini, and T. Zang, An efficient Monte Carlo method for optimal control problems with uncertainty, Computational Optimization and Applications, vol.26, issue.2, pp.219-230, 2003.

Y. Cao, Numerical solutions for optimal control problems under SPDE constraints, 2006.

J. Ching, J. L. Beck, and K. A. Porter, Bayesian state and parameter estimation of uncertain dynamical systems, Elsevier Probabilistic Engineering Mechanics, vol.21, issue.1, pp.81-96, 2006.

F. Duck, Physical Properties of Tissue: A Comprehensive Reference Book, 1990.

M. Eiermann, O. Ernst, and E. Ullmann, Computational aspects of the stochastic finite element method Computing and Visualization in, Science, issue.1, pp.3-15, 2007.

T. Faes, D. Van, D. Munck, and R. Heethaar, The electric resistivity of human tissues (100 hz-10 mhz): a meta-analysis of review studies, Physiological measurement, issue.4, pp.1-11, 1999.

M. Fernández and N. Zemzemi, Decoupled time-marching schemes in computational cardiac electrophysiology and ecg numerical simulation, Mathematical biosciences, vol.226, issue.1, pp.58-75, 2010.

S. Gabriel, R. Lau, and C. Gabriel, The dielectric properties of biological tissues: Ii. measurements in the frequency range 10 hz to 20 ghz, Physics in medicine and biology, vol.41, issue.11, pp.22-51, 1996.

S. Geneser, R. Kirby, R. Macleod, and R. Kirby, Application of stochastic finite element methods to study the sensitivity of ecg forward modeling to organ conductivity, Biomedical Engineering, vol.55, issue.1, pp.31-40, 2008.

R. Gulrajani, The forward and inverse problems of electrocardiography, EMBS Magazine, vol.17, issue.5, pp.84-101, 1998.

J. Hadamard, Lectures on Cauchy's problem in linear partial differential equations, 1923.

D. Hamby, A review of techniques for parameter sensitivity analysis of environmental models, The Review of Economics and Statistics, vol.32, issue.2, pp.135-154, 1994.

J. M. Holtzman, On using perturbation analysis to do sensitivity analysis: derivatives versus differences, IEEE Transactions on Automatic Control, vol.37, issue.2, pp.243-247, 1992.

L. Hou, J. Lee, and H. Manouzi, Finite element approximations of stochastic optimal control problems constrained by stochastic elliptic pdes, Elsevier Journal of Mathematical Analysis and Applications, vol.384, pp.87-103, 2011.

O. L. Mâ-itre, M. Reagan, H. Najm, R. Ghanem, and O. Knio, A stochastic projection method for fluid flow: II. random process, Elsevier Journal of Computational Physics, vol.181, issue.1, pp.9-44, 2002.

A. Mugler and H. J. Starkloff, On elliptic partial differential equations with random coefficients, Babes-Bolyai Math, vol.56, issue.2, pp.473-487, 2011.

A. Oosterom and G. Huiskamp, The effect of torso inhomogeneities on body surface potentials quantified using tailored geometry, Journal of electrocardiology, vol.22, issue.1, pp.53-72, 1989.

C. Ramanathan and Y. Rudy, Electrocardiographic imaging: II. Effect of torso inhomogeneities on noninvasive reconstruction of epicardial potentials, electrograms and isochrones, Journal of cardiovascular electrophysiology, vol.12, issue.2, pp.241-252, 2001.

E. Rosseel and G. N. Wells, Optimal control with stochastic PDE constraints and uncertain controls, Computer Methods in Applied Mechanics and Engineering, vol.213, pp.152-167, 2012.

H. Tiesler, R. M. Kirby, D. Xiu, and T. Preusser, Stochastic collocation for optimal control problems with stochastic PDE constraints, SIAM J. Control optim, vol.50, issue.5, pp.2659-2682, 2012.

H. Verbeeck, R. Samson, F. Verdonck, and R. Lemeur, Parameter sensitivity and uncertainty of the forest carbon flux model forug: a Monte Carlo analysis, Tree Physiology, vol.26, issue.1, pp.807-817, 2006.

J. Wan and N. Zabaras, A Bayesian approach to multiscale inverse problems using the sequential Monte Carlo method, Inverse Problems, vol.27, issue.10, pp.105004-105029, 2011.

F. Weber, D. Keller, S. Bauer, G. Seemann, C. Lorenz et al., Predicting tissue conductivity influences on body surface potentialsan efficient approach based on principal component analysis, Biomedical Engineering IEEE Transactions, vol.58, issue.2, pp.256-273, 2011.

N. Wiener, The homogeneous chaos, Am. J. Math, vol.60, pp.897-936, 1938.

D. Xiu and G. Karniadakis, Modeling uncertainty in flow simulations via generalized polynomial chaos, J.Comput.Phys, vol.187, issue.1, pp.137-167, 2003.

N. Zabaras and B. Ganapathysubramanian, A scalable framework for the solution of stochastic inverse problems using a sparse grid collocation approach, Elsevier Journal of Computational Physics, vol.227, issue.9, pp.4697-4735, 2008.