Publications


Papers on:

  • Hybrid Inverse Problems
  • Inverse Transport Problems and Integral Geometry
  • Inverse Problems Theory and Algorithms

  • Stochasticity of PDE solutions in random media
  • Imaging and Time Reversal in random media
  • Models of Wave Propagation in Random Media

  • Macroscopic Models in Transport
  • Probabilistic representations & Monte Carlo
  • Numerical Analysis

  • Hybrid Inverse Problems

  • Reconstruction of constitutive parameters in isotropic linear elasticity from noisy full-field measurements, (with C. Bellis, S. Imperiale and F. Monard), submitted
  • Reconstruction of complex-valued tensors in the Maxwell system from knowledge of internal magnetic fields, (with C. Guo), submitted
  • Hybrid Inverse Problems for a System of Maxwell's Equations, (with T. Zhou), submitted
  • Inverse anisotropic conductivity from internal current densities, (with C. Guo and F. Monard), submitted
  • Local Inversions in Ultrasound Modulated Optical Tomography, (with S. Moskow), submitted
  • Linearized internal functionals for anisotropic conductivities, (with C. Guo and F. Monard), submitted
  • The Levenberg-Marquardt Iteration for Numerical Inversion of the Power Density Operator, (with W. Naetar, O. Scherzer and J.C. Schotland), J. Inverse and Ill-Posed Probl., 21, 265280, 2013
  • Boundary control of elliptic solutions to enforce local constraints, (with M. Courdurier), J. Differential Equations, 255(6), pp. 1357-1381, 2013
  • Hybrid inverse problems and redundant systems of partial differential equations, To Appear in Contemp. Math., 2013
  • Inverse anisotropic conductivity from power density measurements in dimensions $n\geq3$ (with F. Monard), Comm. Partial Differential Equations, 38(7), pp. 1183-1207, 2013
  • Reconstructions for some coupled-physics inverse problems (with G. Uhlmann), Applied Mathematics Letters, 25(7), pp. 1030-1033, 2012
  • Explicit Reconstructions in QPAT, QTAT, TE, and MRE, ArXiv 2012
  • Reconstruction of coefficients in scalar second-order elliptic equations from knowledge of their solutions (with G. Uhlmann), to appear in C.P.A.M., 2013
  • Inverse anisotropic diffusion from power density measurements in two dimensions (with F. Monard), Inverse Problems 29(8), 084001, 2012
  • Inverse diffusion problem with redundant internal information (with F. Monard), Inverse Problems 29(8), 084001, 2012
  • Hybrid inverse problems and internal functionals (review paper), Inside Out II, MSRI Publications, G. Uhlmann Editor, Cambridge University Press, 2012
  • Cauchy problem for Ultrasound Modulated EIT , to appear in Analysis & PDE, 2013
  • Inverse diffusion from knowledge of power densities (with E. Bonnetier, F. Monard and F. Triki), Inverse Problems and Imaging 7(2), pp. 353-375, 2013
  • On Multi-spectral quantitative photoacoustic tomography (with K. Ren), Inverse Problems, 28, 025010, 2012
  • Multiple-source quantitative photoacoustic tomography (with K. Ren), Inverse Problems, 27(7), 075003, 2011
  • Non-uniqueness result for a hybrid inverse problem (with K. Ren), In Tomography and Inverse Transport Theory, (G. Bal, D. Finch, P. Kuchment, P. Stefanov, G. Uhlmann (Editors)), Contemporary Mathematics, 559, pp. 29-38, 2011
  • Quantitative Thermo-acoustics and related problems (with K. Ren, G. Uhlmann and T. Zhou), Inverse Problems, 27(5), 055007, 2011
  • Inverse Scattering and Acousto-Optic Imaging (with J.C. Schotland), Phys. Rev. Letters, 104, 043902, 2010
  • Inverse Diffusion Theory of Photoacoustics (with G. Uhlmann), Inverse Problems, 26(8), 085010, 2010
  • Inverse Transport Theory of Photoacoustics (with A. Jollivet and V. Jugnon), Inverse Problems, 26, 025011, 2010
  • Inverse Transport Problems and Problems of Integral Geometry

  • Inverse Transport with isotropic time harmonic sources (with F. Monard), SIAM J. Math. Anal., 44, pp.134-161, 2012
  • Angular average of time-harmonic transport solutions (with A. Jollivet, I. Langmore and F. Monard), Comm. Partial Differential Equations, 36(6), pp. 1044-1070, 2011
  • Combined source and attenuation reconstructions in SPECT (with A. Jollivet), to appear in Contemporary Mathematics, 559, pp. 13-28, 2011
  • An accurate solver for forward and inverse transport (with F. Monard), J. Comp. Phys., 229, pp. 4952-4979, 2010
  • Inverse Transport Theory and applications (review paper), Inverse Problems, 25, 055006, 2009
  • Time-dependent angularly averaged inverse transport (with A. Jollivet), Inverse Problems, 25, 075010, 2009. (long version with additional proofs and results arXiv:0902.3432 )
  • Approximate stability in inverse transport (with A. Jollivet), in Biomedical Mathematics, Ed. Y. Censor, M. Jiang, G. Wang, Medical Physics Publishing, Wisconsin, 2010
  • Stability for time dependent inverse transport (with A. Jollivet), SIAM J. Math. Anal., 42(2), pp. 679-700, 2010
  • Stability estimates in stationary inverse transport (with A. Jollivet), Inverse Probl. Imaging, 2(4), pp. 427-454, 2008
  • Inverse transport from angularly averaged measurements and time harmonic isotropic sources, in Mathematical Methods in Biomedical Imaging and Intesity-Modulated Radiation Therapy, Ed. Y. Censor, M. Jiang, A.K. Louis, CRM Series, Scuola Normale Superiore Pisa, Italy, pp. 19-35, 2008
  • Inverse transport with isotropic sources and angularly averaged measurements, (with I. Langmore and F. Monard), Inverse Probl. Imaging, 2(1), pp. 23-42, 2008
  • Transport- and diffusion-based optical tomography in small domains: a comparative study, (with K. Ren and A. Hielscher), Applied Optics, 46(27), pp. 6669-6679, 2007
  • Inverse source problems in transport equations, (with A. Tamasan), SIAM J. Math. Anal., 39(1), pp. 57-76, 2007
  • Frequency Domain Optical Tomography Based on the Equation of Radiative Transfer, (with K. Ren and A. Hielscher), SIAM J. Sci. Comput., 28, pp. 1463-1489, 2006
  • Ray Transforms in Hyperbolic Geometry, J. Math. Pures Appl., 84(10), pp. 1362-1392, 2005
  • Atmospheric Concentration Profile Reconstructions from Radiation Measurements (with K. Ren), in Inverse Problems, 21(1), pp. 153-168, 2005
  • Fast numerical inversion of the attenuated Radon transform with full and partial measurements (with P. Moireau), Inverse Problems, 20(4), pp. 1137-1164, 2004
  • On the attenuated Radon transform with full and partial measurements, Inverse Problems, 20(2), pp. 399-418, 2004
  • Inverse problems for homogeneous transport equations. Part I: One-dimensional case, Inverse Problems, 16 , pp. 997-1011, 2000
  • Inverse problems for homogeneous transport equations. Part II: Multidimensional case, Inverse Problems, 16 , pp. 1013-1028, 2000
  • Inverse Problem Theory and Algorithms

  • Part I and Part II Long version of the article: Multi-Pixel Retrieval of Structural and Optical Parameters in a 2D Scene with a Path-Recycling Monte Carlo Forward Model and a New Bayesian Inference Engine (with I. Langmore and A. Davis), IEEE Trans. Geosci. Remote Sensing, 51(5), pp.9203-2919, 2013
  • Bayesian Inverse Problems with Monte Carlo Forward Models (with I. Langmore and Y. Marzouk), Inverse Problems Imaging, 7(1), pp. 81-105, 2013
  • Small volume expansions for elliptic equations (with O. Pinaud), Asymptotic Analysis, 70(1-2), pp. 13-50, 2010
  • Physics-based models for measurement correlations. Application to an inverse Sturm-Liouville problem (with K. Ren), Inverse Problems, 25, 053001, 2009
  • Reconstruction of singular surfaces by shape sensitivity analysis and level set method (with K. Ren), Math. Models Methods Appl. Sci, 16(8), pp. 1347-1373, 2006
  • Reconstructions in impedance and optical tomography with singular interfaces, Inverse Problems, 21(1), pp. 113-132, 2005
  • On the reconstruction of diffusions using a single first-exit time distribution (with T. Chou), Inverse Problems, 20(4), pp. 1053-1066, 2004
  • Optical tomography of small volume absorbing inclusions, Inverse Problems, 19(2), pp. 371-386, 2003
  • Stochasticity of PDE solutions with Random Coefficients. Applications in Uncertainty Quantification

  • Limiting models for equations with large random potential; a review (with Y. Gu), submitted 2013
  • Convergence to SPDE of the Schroedinger equation with large, random potential (with Ningyao Zhang), to appear in Comm. Math. Sci., 2013
  • Corrector Analysis of a Heterogeneous Multi-scale Scheme for Elliptic Equations with Random Potential (with W. Jing), to appear in M2AN, 2013
  • Homogenization of the Schroedinger equation with large, random potential (with Ningyao Zhang), to appear in Stochastics & Dynamics, 2013.
  • Random Homogenization and Convergence to Integrals with respect to the Rosenblatt Process (with Y. Gu), J. Diff. Equ., 253(4), pp. 1069-1087, 2012
  • Corrector Theory for Elliptic Equations with Long-range Correlated Random Potential (with J. Garnier, W. Jing, and Y. Gu), Asymptotic Analysis, 77(3-4), pp. 123-145, 2012
  • Large Deviation Theory for a Homogenized and "Corrected" Elliptic ODE (with R. Ghanem and I. Langmore), J. Differential Equations, 251(7), pp. 1864-1902, 2011
  • Corrector theory for MsFEM and HMM in random media (with W. Jing), Multiscale Model. Simul., 9, pp. 1549-1587, 2011
  • Convergence to Homogenized or Stochastic Partial Differential Equations, Appl Math Res Express, 2011(2), pp. 215-241, 2011
  • Corrector theory for elliptic equations in random media with singular Green's function. Application to random boundaries (with W. Jing), Comm. Math. Sci., 9(2), pp. 383-411, 2011
  • Homogenization and Corrector Theory for Linear Transport in Random Media (with W. Jing), Disc. Cont. Dyn. Syst. A, 28(4), pp. 1311 - 1343, 2010
  • Fluctuation theory for radiative transfer in random media (with W. Jing), Journal of Quantitative Spectroscopy and Radiative Transfer , 112(4), pp. 660-670, 2011
  • Homogenization with large spatial random potential, Multiscale Model. Simul., 8, pp. 1484-1510, 2010
  • Convergence to SPDEs in Stratonovich form, Comm. Math. Phys., 212(2), pp. 457-477, 2009
  • Central limits and homogenization in random media, (long version with more detailed proofs arXiv:0710.0363 ), Multiscale Model. Simul., 7(2), pp. 677-702, 2008
  • Random integrals and correctors in homogenization (with J. Garnier, S. Motsch, and V. Perrier), Asymptotic Analysis, 59(1-2), pp. 1-26, 2008
  • Homogenization in random media and effective medium theory for high frequency waves, Disc. Cont. Dyn. Syst. B, 8(2), pp. 473-492, 2007
  • Imaging and Time Reversal in Random Media. Theoretical, numerical, experimental results

  • Correlations of heterogeneous wave fields propagating in homogeneous media (with O. Pinaud), To appear in Contemporary Mathematics, 2013
  • Imaging using transport models for wave-wave correlations (with O. Pinaud), Math. Models Methods Appl. Sci, 21(3), pp. 1071-1093, 2011
  • Inverse Problems in random media: a kinetic approach, J. Phys. Conf. Series, 124, 012001, 2008
  • Transport-based imaging in random media (with K. Ren), SIAM J. Appl. Math., 68(6), pp. 1738-1762, 2008
  • Experimental validation of a transport-based imaging method in highly scattering environments (with L. Carin, D. Liu, and K. Ren), Inverse Problems , 26(3), pp. 2527-2539, 2007
  • Kinetic Models for Imaging in Random Media (with O. Pinaud), SIAM Multiscale Model. Simul. , 6(3), pp. 792-819, 2007
  • Electromagnetic Time-Reversal Imaging in Changing Media: Experiment and Analysis (with D. Liu, S. Vasudevan, J. Krolik, and L. Carin), IEEE Trans. Anten. and Prop., 55(2), pp. 344-354, 2007
  • Stability of time reversed waves in changing media (with L.Ryzhik), Disc. Cont. Dyn. Syst. A , 12(5), pp. 793-815, 2005
  • Time Reversal in Changing Environment (with R.Verastegui), SIAM Multiscale Model. Simul. , 2(4), pp. 639-661, 2004
  • Time reversal based detection in random media (with O. Pinaud), Inverse Problems, 21(5), pp. 1593-1620, 2005
  • Time Reversal for Classical Waves in Random Media (with L.Ryzhik), C. R. Acad. Sci. Paris, Serie I, 333, pp. 1041-1046, 2001
  • Time Reversal and refocusing in Random Media (with L.Ryzhik), SIAM J. Appl. Math., 63(5), pp. 1475-1498, 2003
  • Models of Wave Propagation in Random Media

  • Analysis of the double scattering scintillation of waves in random media (with O. Pinaud), to appear in Comm. Partial Differential Equations, 2013
  • Kinetic limits for waves in a random medium (review paper) (with T. Komorowski and L. Ryzhik) Kinetic Related Models, 3(4), pp. 529 - 644, 2010
  • Asymptotics of the phase of the solutions of the random Schroedinger equation (with T. Komorowski and L. Ryzhik), Archives for Rational Mechanics and Analysis, 200(2), pp. 613-664, 2011
  • Single scattering estimates for the scintillation function of waves in random media (with I. Langmore and O. Pinaud), J. Math. Phys., 51, 022903, 2009
  • Dynamics of wave scintillation in random media (with O. Pinaud), Comm. Partial Differential Equations, 35, pp. 1176-1235, 2010
  • Self-averaging of kinetic models for waves in random media (with O. Pinaud), (Some errors corrected compared to printed version) Kinetic Related Models, 1(1), pp. 85-100, 2008
  • Accuracy of transport models for waves in random media (with O. Pinaud), Wave Motion, 43(7), pp. 561-578, 2006
  • Wave field correlations in weakly mismatched random media (with L.Ryzhik), Stochastics & Dynamics, 6(3), pp. 301-328, 2006
  • Kinetics of scalar wave fields in random media, Wave Motion, 43, pp. 132-157, 2005
  • Time splitting for wave equations in random media (with L.Ryzhik), M2AN Math. Model. Numer. Anal. , 38(6), pp. 961-988, 2004
  • Time splitting for the Liouville equation in a random medium (with L.Ryzhik), Comm. Math. Sci. , 2(3), pp. 515-534, 2004
  • On the self-averaging of wave energy in random media, SIAM Multiscale Model. Simul. , 2(3), pp. 398-420, 2004
  • Self-averaging of Wigner transforms in random media (with T. Komorowski and L. Ryzhik), Comm. Math. Phys., 242(1-2), pp. 81-135, 2003
  • Self-averaging in time reversal for the parabolic wave equation (with G. Papanicolaou and L. Ryzhik), Stochastics and Dynamics , 2(4), pp. 507-532, 2002
  • Radiative transport limit for the random Schroedinger equation (with G. Papanicolaou and L. Ryzhik) Nonlinearity, 15(2), pp. 513-529, 2002
  • Capillary-gravity wave transport over spatially random drift (huge file!) (with T.Chou), Wave Motion, 35 , pp. 107-124, 2002
  • Wave transport for a scalar model of the Love waves (with L.Ryzhik), Wave Motion, 36, pp. 49-66, 2002
  • Wave transport along surfaces with random impedance (with V.Freilikher, G.Papanicolaou and L.Ryzhik), Phys. Rev. B, 62(10), pp. 6228-6240, 2000
  • Radiative Transport in a Periodic Structure (with A.Fannjiang, G.Papanicolaou and L.Ryzhik), Journal of Statistical Physics, 95, pp. 479-494, 1999
  • Diffusive Energy Scattering from Weakly Random Surfaces (with G.Papanicolaou and L.Ryzhik), Journal of Mathematical Physics, 40, pp. 4813-4827, 1999
  • Transport Theory for Acoustic Waves with Reflection and Transmission at Interfaces (with J.B.Keller, G.Papanicolaou and L.Ryzhik), Wave Motion, 30, pp. 303-327, 1999
  • Macroscopic Models in Transport Theory

  • A corrector theory for diffusion-homogenization limits of linear transport equations (with Naoufel Ben-Abdallah and Marjolaine Puel), SIAM. J. Math. Anal., 44(6), pp. 3848-3973, 2012
  • Radiative transfer equations with varying refractive index: a mathematical perspective, J. Opt. Soc. Am. A, 23(7), pp. 1639-1644, 2006
  • Transport approximations in partially diffusive media, Lecture Notes in Computational Science and Engineering; Ed. F. Graziani, Proceedings of the Computational Methods in Transport Workshop, Lake Tahoe, September 2004, 48, pp. 373-400, 2006
  • Generalized diffusion model in optical tomography with clear layers (with K. Ren), J. Opt. Soc. Amer. A, 20(12), pp. 2355-2364, 2003
  • Transport through diffusive and non-diffusive regions, embedded objects, and clear layers, SIAM J. Appl. Math., 62(5), pp. 1677-1697, 2002
  • Particle transport through scattering regions with clear layers and inclusions, J. Comp. Phys., 180(2), pp. 659-685, 2002
  • Coupling of transport and diffusion models in linear transport theory (with Y. Maday), M2AN Math. Model. Numer. Anal., 36(1), pp. 69-86, 2002
  • Homogenization and localization in locally periodic transport (with G. Allaire and V. Siess) ESAIM Contr. Op. Ca. Va., 8, pp. 1-20, 2002
  • Homogenization of a spectral equation with drift in linear transport, ESAIM Contr. Op. Ca. Va., 6(26), pp. 613-627, 2001
  • Diffusion Approximation of Radiative Transfer Equations in a Channel, Transport Theory and Statistical Physics, 30(2-3), 2001
  • Diffusion Approximation of Radiative Transfer Problems with Interfaces (with L.Ryzhik), SIAM, J. Appl. Math., 60(6), pp.1887-1912, 2000
  • Homogenization of the criticality spectral equation in neutron transport (with G. Allaire), M2AN Math. Model. Numer. Anal., 33(4), pp. 721-746, 1999
  • First-order Corrector for the Homogenization of the Criticality Eigenvalue Problem in the Even Parity Formulation of the Neutron Transport, SIAM J. Math. Anal., 30, pp. 1208-1240, 1999
  • Boundary Layer Analysis in the Homogenization of Neutron Transport Equations in a Cubic Domain, Asymptotic Analysis, 20(3-4), pp. 213-239, 1999
  • Probabilistic Representation of Radiative Transfer and Monte Carlo Methods

  • A hybrid (Monte-Carlo/deterministic) approach for multi-dimensional radiation transport (with A.B. Davis and I. Langmore), Journal of Computational Physics, 230(20), pp. 7723-7735, 2011. See also the longer version: Importance Sampling and Adjoint Hybrid Methods in Monte Carlo Transport with Reflecting Boundaries (with I. Langmore).
  • Probabilistic Theory of Transport Processes with Polarization (with G.Papanicolaou and L.Ryzhik), SIAM, J. Appl. Math., 60(5), pp.1639-1666, 2000
  • Polarization Effects of Seismic Waves on the Basis of Radiative Transport Theory (with M.Moscoso), Geophys. J. Int., 142(2), pp. 571-585, 2000
  • Theoretical and Numerical Analysis of Polarization for Time Dependent Radiative Transfer Equations (with M.Moscoso), Journal of Quantitative Spectroscopy and Radiative Transfer, 70(1), pp. 75-90, 2001
  • Radiative Transfer for Wave Propagation in Random Media. Monte Carlo Simulations of Seismic Waves (with M.Moscoso), in Mathematical and numerical aspects of wave propagation (Santiago de Compostela, 2000), pp. 559-563, SIAM, Philadelphia, PA, 2000
  • Numerical Analysis

  • Symplectic Parareal (with Q. Wu), Proceedings of DD17, 2008
  • Parallelization in time of (stochastic) ordinary differential equations
  • On the Convergence and the Stability of the Parareal Algorithm to solve Partial Differential Equations, Proceedings of DD15, Berlin, Vol. 40, LNCSE Series, Springer Verlag, Berlin, pp. 425-432, 2004
  • A "parareal" time discretization for non-linear PDE's with application to the pricing of an American put (with Y. Maday), Proceedings of the Workshop on Domain Decomposition, Zurich, Switzerland, LNCSE Series, Springer Verlag, 2001
  • Fourier Analysis of Diamond Discretization in Particle Transport, Calcolo, 38(3), pp. 141-172, 2001
  • Spatially Varying Discrete Ordinates Methods in XY-Geometry, Math. Models Meth. Appl. Sci., 10(9), pp. 1277-1303, 2000
  • Discrete Ordinates Methods in xy Geometry with Spatially Varying Angular Discretizations (with X. Warin) Nuclear Science and Engineering: 127(2), pp. 169-181, 1997



  • Guillaume Bal