Morgane Henry - Laboratoire Jean Kuntzmann

Morgane Henry
Ph.D. student in Applied Mathematics
Applied Mathematics Université Grenoble Alpes, Laboratoire Jean Kuntzmann
Office address Laboratoire Jean Kuntzmann, Université Grenoble Alpes,
UMR 5524 CNRS, BP 53, 38041 Grenoble Cedex 9, France
Home address
Phone
Email
Home page
3 bis rue Elisée Reclus, 38100 Grenoble, France
+ 33 6 29 06 09 98
[email protected]
www-ljk.imag.fr/membres/Morgane.Henry/
Education
Since Sept. Ph.D. in Applied Mathematics, Laboratoire Jean Kuntzmann, Université Grenoble Alpes, Optimal
2012 Transport and Wavelets: new algorithms and applications to image processing.
Supervisors: Emmanuel Maitre and Valérie Perrier.
Sept. 2010– Master of Science in Mathematics and Applications, Université de Haute-Alsace, Mulhouse,
June 2012 France, Pass with honors and CROUS merit scholarship.
Second year carried out at Montreal, Canada, classes at McGill University, Ecole Polytechnique de Montréal,
and Université de Montréal.
Sept. 2007– Bachelor of Mathematics and Informatics, Université de Haute-Alsace, Mulhouse, France, Pass
June 2010 with honors.
Preparatory class for entrance to Grandes Ecoles (Mathematics and Physics), Lycée Paul Cézanne (Aix-enProvence, France)
Research Experience
Since Sept. Ph.D. in Applied Mathematics, Laboratoire Jean Kuntzmann, Grenoble, France, Optimal Transport
2012 and Wavelets : new algorithms and applications to image processing.
Developing new algorithms, sparsely decomposing on wavelet bases or using Helmholtz-Hodge decomposition,
reducing the problem to a minimal surfaces equation, using primal-dual algorithms, implementing on Matlab,
FreeFem ++ and C++ with OpenMP.
June 2013 Semaine d’étude Maths-Entreprises (Week of study Mathematics-Industry), Laboratoire Jean
Kuntzmann, Grenoble, France, Statistical analysis of analogue electronic flaws for Halias company.
Working in team, presenting the results and writing a synthesis report [P3].
Jan. 2012– Internship in Mathematics and applications, Université de Montréal, Montreal, Canada, ModJune 2012 elling a fluid flow with immersed membranes.
Advisor: Robert Owens. Realizing a scientific and technology watch, establishing a model for fluid flow with
immersed membranes, computing with Matlab in 3D, comparing our results with empiric studies.
Jan. 2011– Internship in Mathematics and applications, Université de Haute-Alsace, Mulhouse, France,
June 2011 Advisors: Samir Akesbi and Cornel Murea. Modelling elastic materials and fluid flow. .
Providing a bibliography of elastic theory (linear and non linear) and of Newtonian fluid flow theory, computing
with FreeFem++ the elastic material deformation and the fluid flow.
Morgane HENRY • H +33 6 29 06 09 98 • B [email protected]
Laboratoire Jean Kuntzmann – Université Grenoble Alpes
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Research Interests
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Optimal Transport
Image Processing
Fluid Mechanics
Fluid-Structure Interaction
Ph.D. Project
My Ph.D. work deals with the resolution of a dynamical optimal transport problem and its application in image
interpolation in the project ANR TOMMI (ANR-11-BS01-014-01).
Thesis title
Optimal transport and wavelets : new algorithms and applications to images
Key words
Convex optimisation, optimal transport, proximal splitting, image processing, Helmholtz-Hodge decomposition,
minimal surfaces equation, divergence-free wavelets
Context
Optimal transport has numerous applications in various domains and in particular in image processing. Minimizing
the energy between two densities, it allows one to define a distance (the Wasserstein distance) between two densities.
Developing new efficient algorithms is still a challenge, especially in the case of images used in real applications.
During this Ph.D., we studied the Benamou-Brenier formulation, which placed the problem in the context of fluid
mechanics by adding a time dimension. The minimization of the energy, depending on the mass and the density
in the constraint space is done using an augmented Lagrangian. The existing algorithms need to project onto the
divergence-free constraint at each iteration. This amounts to solving a 3D Poisson equation at each iteration for a
2D image. To reduce the cost of the algorithm, we worked in this Ph.D. directly in the constraint space to minimize
the functional, and thus we do not have to solve the Poisson equation.
Contributions
The constraint is preserved by the decomposition of the divergence-free vector made by the moment and the density
which depend on the time and the space. We first developed descent algorithms using the divergence-free wavelet
decomposition. This approach was in fact too complex but gave us the idea to project the unknown vectors using
the Helmholtz-Hodge decomposition. This allows us to rewrite the Benamou-Brenier functional in a stream function
formulation. For 1D images, the Euler Lagrange equation is equivalent to a minimal surface equation. We then
wanted to develop a similar approach for 2D images but the properties used in 1D are not valid in 2D. Finally,
we applied the primal-dual algorithm detailed by Chambolle and Pock, which can be easily adapted to finding the
minimum of our new functional. This algorithm is nowadays widely used and allows one a simple implementation and
an easy parallelization.
Conclusion and perspectives
Two algorithms were introduced for the optimal transport between two images 1D or 2D, which respect the divergencefree constraint throughout the algorithm and allows one not to solve a Poisson equation at each iteration. Moreover,
this method is easy to implement and faster than state of the art algorithms. We tested it on images of sizes met in
the applications. Improvements can still be made by changing the divergence-free decomposition used or changing
the algorithm to minimize the obtained functional.
Morgane HENRY • H +33 6 29 06 09 98 • B [email protected]
Laboratoire Jean Kuntzmann – Université Grenoble Alpes
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Research Activity
Publications
[P1] Henry, M., Maitre, E., Perrier, V., “Optimal Transport using HelmHoltz-Hodge decomposition and Primal-Dual
Algorithm”, in preparation, 2015.
[P2] Henry, M., Maitre, E., Perrier, V., “Optimal Transport using HelmHoltz-Hodge decomposition and first order
Primal-Dual Algorithm”, Icip 2015 accepted, 2015 (hal-01134194).
[P3] Fageot, J., Henry, M., Huet A., Mazo G., Veys S., “Analyse statistique des défauts en électronique analogique”,
Semaine d’Etude Mathématiques et Entreprises 6. 2013 (hal-00933235).
Conferences
[C1] Henry, M., Maitre, E., Perrier, V., “Primal-dual formulation of the optimal transport problem using divergencefree vector field decomposition”, Workshop Optimal Transport: Aspects Numériques et Applications, IMB, Université
de Bordeaux, 2015.
[C2] Henry, M., Maitre, E., Perrier, V.,“Optimal Transport using HelmHoltz-Hodge decomposition and first order
Primal-Dual Algorithm”, Icip 2015, Québec City, Canada ,2015.
[C3] Henry, M., Maitre, E., Perrier, V., “Algorithme primal-dual et décomposition de Helmholtz-Hodge pour le calcul
du transport optimal”, Congrès SMAI, Les Karellis, 2015.
[C4] Henry, M., Maitre, E., Perrier, V., “Optimal Transport using HelmHoltz-Hodge decomposition and Primal-Dual
Algorithm”, RICAM, Linz, Austria, 2014.
[C5] Henry, M., Maitre, E., Perrier, V., “Un lien entre le transport optimal 1D et l’équation des surfaces minimales”,
Poster, Congrès CANUM, Carry-le-Rouet, 2014.
[C6] Henry, M., Maitre, E., Perrier, V., “Transport Optimal et Ondelettes”, Ecole d’été de Peyresq, 2013.
[C7] Henry, M., Maitre, E., Perrier, V., “Transport Optimal et Ondelettes”, Journées Calcul des Variations, 2013.
Summer Schools
Dec. 2014 New Trends in Calculus of Variations: Optimal Transport in the Applied Sciences, Special
Semester, RICAM, Linz, Autriche.
June 2013 New Optimization Techniques : Applications to Signal, Image and Communications, Ecole
d’été de Peyresq, GRETSI et GdR ISIS, Peyresq.
March 2013 Numerical Meetings 2013 "Wavelets and Partial Differential Equations" , Laboratoire Paul
Painlevé, Lille.
Dec. 2012 Introduction to being lecturer and researcher , Collège doctoral Université de Grenoble , Autrans.
Sept. 2012– Numerical Methods for the Flow of Complex Fluids, Université Joseph Fourier, Grenoble.
Dec. 2012
Administrative Activity and Miscellaneous
Since Nov. PhD Student Representative in the Laboratoire Jean Kuntzmann.
2013
Since Nov. Committee member for the self-assessment of Laboratoire Jean Kuntzmann.
2013
Oct. 2013 Member of the organization committee of the Laboratoire Jean Kuntzmann’s stand for the
Fête de la Science.
In collaboration with Institut Fourier, organizing and hosting a stand, creating the communication support and
coordinating the activities around the subject : Cellular automaton.
Morgane HENRY • H +33 6 29 06 09 98 • B [email protected]
Laboratoire Jean Kuntzmann – Université Grenoble Alpes
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Teaching Interests
{ Graduate level numerical methods
{ Undergraduate level analysis
{ Graduate applied mathematics for other sciences
Teaching Activity
Since september 2012, I am a teaching assistant for first year students at the engineering school Ensimag (third year
at university) in Grenoble.
Jan. 2013– Numerical methods (3x18h), Ensimag, Grenoble, France.
June 2015 Content : linear systems resolution, non linear equations, interpolation, numerical integration, ordinary
differential equations, optimization.
I held classes for up to 40 students, held office hours and graded exams.
Jan. 2014– Tutoring in numerical methods (18h), Ensimag, Grenoble, France.
June 2014 I prepared and conducted tutorials for up to 15 students having difficulties in numerical methods.
Sept. 2013– Analysis (2x18h), Ensimag, Grenoble, France.
Dec. 2014 Content : metric spaces, normed vector spaces or Banach spaces, differential calculus and integration, Fourier
transform.
I held tutorials for classes of up to 40 students and graded exams.
Sept. 2012– Introduction to Scilab and Latex (2x18h + 6h), Ensimag, Grenoble, France.
Dec. 2014 I supervised laboratory sessions for up to 40 students, updated the subject and graded the exam. I managed
online support and gathering of reports
Sept. 2012– Applied mathematics for process engineering (36h), Université Joseph Fourier, Grenoble, France.
Dec. 2012 Content : Introduction to Matlab and Comsol Multiphysics, linear algebra, numerical resolution of ODEs,
PDEs.
I supervised and prepared laboratory sessions. I graded all the reports during the semester.
Sept. 2012– Co-supervising of internship for second year students, Ensimag, Grenoble, France.
June 2013 I supervised two students from Ensimag with Emmanuel Maitre. They developed a FreeFem ++ primal dual
algorithm applied to an optimal transport problem. They wrote a report and presented their work in front of a
jury in which I participated.
Sept. 2010– Tutoring in mathematics for first year students at university, Université de Haute-Alsace, MulDec. 2010 house, France.
I held tutorials for up to 10 students, I planed the sessions.
Computer Skills
Op. system Microsoft Windows, Linux, Mac OSX
Mathematics Matlab, Scilab, C++ (OpenMP), FreeFem++, LaTeX, Python, Maple, Mathematica
Internet HTML, CSS
Languages
French Mother tongue
English TOEIC 960/990 in 2011
3 weeks school in Cambridge in 2008
References
{ Emmanuel Maitre, Laboratoire Jean Kuntzmann, Université Grenoble Alpes + 33 4 76 63 57 38 (thesis supervisor)
{ Valérie Perrier, Laboratoire Jean Kuntzmann, Université Grenoble Alpes +33 4 76 51 45 51 (thesis supervisor)
{ Samir Akesbi, Laboratoire de Mathématiques Informatique et Applications, Université de Haute Alsace +33 3 89
33 60 34 (graduate supervisor)
Morgane HENRY • H +33 6 29 06 09 98 • B [email protected]
Laboratoire Jean Kuntzmann – Université Grenoble Alpes
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