Publications

Recent Papers:

Papers before 2019:

Time reversal by time-dependent perturbations , with Mathias Fink and Olivier Pinaud, SIAM J. Appl. Math., 79(3): 754-780, 2019
Continuous bulk and interface description of topological insulators , J. Math. Phys. 60, 081506, 2019
Topological protection of perturbed edge states , Comm. Math. Sci., 27(1):193-225, 2019.
Propagation of singularities for linearised hybrid data impedance tomography , with Kristoffer Hoffmann and Kim Knudsen, IP Vol. 34, 2017
A Dynamical Sparse Grid Collocation Method for Differential Equations Driven by White Noise , with H. Cagan Ozen, ArXiv Preprint
Reconstruction of Cloud Geometry from High-Resolution Multi-Angle Images , with JiaMing Chen and Anthony Davis, I.P.I. Vol. 12(2), 2018
Generalized stability estimates in inverse transport theory , with Alexandre Jollivet, IPI Vol. 12(1), 2018
Critical Points for Elliptic Equations with Prescribed Boundary Conditions , with Giovanni S. Alberti and Michele Di Cristo, ARMA 2017
Photo-acoustic tomography in a rotating measurement setting , with Amir Moradifam, Inverse Problems 2016
A dynamical polynomial chaos approach for long-time evolution of SPDEs , with H. Cagan Ozen, J.C.P. 2017
Fluctuations in the Homogenization of Semilinear Equations with Random Potentials , with Wenjia Jing, Comm. Partial Differential Equations, 42 (2016), no.12, pp. 1839--1859
Ultrasound modulated bioluminescence tomography and controllability of the radiative transport equation , with Francis J. Chung and John Schotland, SIAM J. Math. Anal., 48(2), 1332–1347, 2016

2011 Course on Inverse Problems: Lecture Notes

Papers (before 2014) 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), Inverse Problems, Volume 30, Number 12 (2014)
Reconstruction of complex-valued tensors in the Maxwell system from knowledge of internal magnetic fields, (with C. Guo), Inverse Problems and Imaging, Pages: 1033 - 1051, Volume 8, Issue 4, November 2014
Hybrid Inverse Problems for a System of Maxwell's Equations, (with T. Zhou), Inverse Problems, Volume 30, Number 5, May 2014
Inverse anisotropic conductivity from internal current densities, (with C. Guo and F. Monard), Inverse Problems, Volume 30, Number 2, January 2014
Local Inversions in Ultrasound Modulated Optical Tomography, (with S. Moskow), Inverse Problems, Volume 30, Number 2, January 2014
Linearized internal functionals for anisotropic conductivities, (with C. Guo and F. Monard), Inverse Problems & Imaging, 2014, Vol. 8 Issue 1, pp.1-22
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, 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), 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 , 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), Comm. Math. Sci., 2013
Convergence to SPDE of the Schroedinger equation with large, random potential (with Ningyao Zhang), in Comm. Math. Sci., 2013
Corrector Analysis of a Heterogeneous Multi-scale Scheme for Elliptic Equations with Random Potential (with W. Jing), M2AN, 2013
Homogenization of the Schroedinger equation with large, random potential (with Ningyao Zhang), 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), 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), 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 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