### Publications

#### Recent Papers:

- Topological protection of perturbed edge states , submitted
- Propagation of singularities for linearised hybrid data impedance tomography , with Kristoffer Hoffmann and Kim Knudsen, submitted
- A Dynamical Sparse Grid Collocation Method for Differential Equations Driven by White Noise , with H. Cagan Ozen, Preprint
- Generalized stability estimates in inverse transport theory , with Alexandre Jollivet, submitted
- 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
- Reconstruction of Cloud Geometry from High-Resolution Multi-Angle Images , with JiaMing Chen and Anthony Davis, to appear in I.P.I.
- 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 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