

Adaptivity for Natural Images and Textures
Representations
The NatImages team tackles the difficult
problem of extracting relevant information from natural
images and textures. NatImages focuses on both sparse and
variational methods to extract the complex structures of
natural images and textures. The geometry of the datasets
one encounters in video watermarking, cortical imaging and
astrophysical imaging does not correspond to simple concepts
such as edges or oscillating textures. This complex geometry
calls for adaptive tools to extend traditional methods used
routinely in image processing: variational regularization
(total variation models and extensions) and sparse decompositions
(wavelet orthogonal bases and extensions). The NatImages
project is a unique chance to develop new adaptive tools
to capture the geometry of natural images and textures.



Team Members.
Research.
The goal of NatImage is to bring both variationalbased
and sparsitybased methods to an adaptive setting in order to unlock
several major problems in video watermarking, cortical imaging and astrophysical
imaging.
The following images shows examples of natural images,
textures, surfacic and movie data that are processed by the NatImage
project.



Wood texture 
Optical stimulus 
Cortical pattern 



Galaxy NGC2997 
HST image of A370 
CMB map on the sphere 
Each kind of data exhibit several kinds of morphological
diversity, that can be exploited thanks to the design of various adaptive
sparse decompositions and variational energies.
Postdoctoral and Master Students.

GuiSong Xia
(supervisors: G. Peyré), Postdoc, 1st April 2011  31 Dec. 2011, Gaussian modeling of dynamic textures.

Julien Rabin
(supervisors: J. Fadili and C. Chesneau), Postdoc, 1st Sept. 2010  31 Aout 2011, Local behavior of sparse regularization.

Julien Rabin
(supervisor: G. Peyré), Postdoc, 1st Novembre 2010  31 Aout 2010, Texture modeling with optimal transport.

Pierre Maurel
(supervisors: J.F. Aujol and G. Peyré), Postdoc, 1st Jan. 2009  31 Dec. 2009, Adapted Hilbert spaces for
the modeling of locally parallel textures, with application to medical imaging.

Erwan Deriaz
(supervisor: J.L. Starck), Postdoc, 1st Jan. 2009  31 Aug. 2009, Source separation in astophysical imaging.

Nicolas Schmidt
(supervisor: G. Peyré and Y. Fregnac), Master, 15 April 2009  15 Sept. 2009,
Separation of propagating waves in the visual cortex.
Collaborators.
 Application to neurosciences: Yves Frégnac (UNICCNRS
GifsurYvette)
 Compressive computations: Laurent Demanet (Stanford)
 Applications to astrophysics: Jérôme
Bobin and Yassir Moudden
(CEA Saclay)
 Nonlocal energies: Antoni
Buades (CNRS)
 Spatial adaptivity and texture modelling: Yann Gousseau and Vincent Duval
(TelecomParis Tech)
NatImages Meetings.
A=Aujol, C=Chesneau, Co=Cohen, D=Dossal, F=Fadili, P=Peyré,
S=Starck.
 Kickoff meeting (talks by all members), 1920 Janvier 2009, Paris, [All]
 Working meeting (sparsity and compressed sensing), 1112 March 2009, Paris, [P,F,D]
 Working meeting (sparsity and compressed sensing), 9 Avril 2009, Paris, [P,F,D,C]
 Working meeting (sparsity and compressed sensing), 2326 Juin 2009, Paris, [P,F,D]
Talks.
 ICIP'09 (Workshop on sparsity), 711 Nov. 2009, Le Caire, [F,S]
 SMAI'09 (minisymposium on Compressed Sensing), 28 Mai 2009, Nice, [P,D]
 Workshop (Approximation and optimization in image restoration and reconstruction), 28 Janvier 2009, Porquerolles, [F,P]
 Conference (GRETSI09), 811 Sept. 2009, Dijon, [F,P,A,S]
 Workshop (Geometrical Method in Mathematical Imaging), 910 Oct. 2009, Munich, [F,P]
 Conference (SIAM Conference on Imaging Science), 1114 Avril 2010, SanDiego, [A,F,P,S]
Journal Publications.
 Wavelet estimation of the derivatives of an unknown function from a convolution model [HAL]
Christophe Chesneau, Preprint Hal00399604, 2009.
 Some firstorder algorithms for total variation based image restoration
JeanFrancois Aujol, Journal of Mathematical Imaging and Vision, 34(3), p. 307327, July 2009.
 The TVL1 model: a geometric point of view
V. Duval, JeanFrancois Aujol and Y. Gousseau, CMLA Preprint 200908, April 2009.
 Total Variation Projection with First Order Schemes [HAL]
Jalal Fadili and Gabriel Peyré, Preprint Hal00380491, May 2009.
 Astronomical Data Analysis and Sparsity: from Wavelets to Compressed Sensing
JeanLuc Starck and J. Bobin, to appear in Proccedings of the IEEE, 2009.
 Image decomposition and separation using sparse representations: an overview
Jalal Fadili, JeanLuc Starck , J. Bobin and Y. Moudden, to appear in Proccedings of the IEEE, 2009.
 Source Detection Using a 3D Sparse Representation: Application to the Fermi Gammaray Space Telescope
JeanLuc Starck , Jalal Fadili, S. Digel , B. Zhang and J. Chiang, Astronomy and Astrophysics, in press, 2009.
Conference Publications.
 Best Basis Denoising with Nonstationary Wavelet Packets [HAL]
Nizar Ouarti and Gabriel Peyré, Proceedings of ICIP'09, Nov. 2009.
 Total Variation Projection with First Order Schemes [HAL]
Jalal Fadili and Gabriel Peyré, Proceedings of ICIP'09, Nov. 2009.
 Sparsity constraints for hyperspectral data analysis
J. Bobin, Y. Moudden, JeanLuc Starck and Jalal Fadili, Proc. of SPIE 09, Wavelet XIII, 2009.
 JeanLuc Starck , J. Bobin, N. Barbey and M. Sauvage
Compressed Sensing and the ESA Herschel Projet, Proc. SPIE 09, Wavelet XIII, 2009.
 J. Schmitt, JeanLuc Starck , Jalal Fadili, I. Grenier and J.M. Casandjian
Poisson denoising on the sphere, Proc. of SPIE 09, Wavelet XIII, 2009.
 A. Woizelle, JeanLuc Starck and Jalal Fadili
3D Inpainting using sparse representations, Proc. of SPIE 09, Wavelet XIII, 2009.
 A Numerical Exploration of Compressed Sampling Recovery [HAL]
Charles Dossal, Gabriel Peyré and Jalal Fadili, Proceedings of SPARS'09, Apr. 2009.
 Algorithmes de premier ordre pour la projection sur une contrainte de variation totale [HAL]
Gabriel Peyré and Jalal Fadili, Proceedings of Gretsi'09, Sept. 2009.
 Extraction de textures localement paralleles par un espace de Hilbert adapté [HAL]
Pierre Maurel, JeanFrancois Aujol and Gabriel Peyré, Proceedings of Gretsi'09, Sept. 2009.
 Compression d'images par triangulations géodésiques anisotropes [HAL]
Sébastien Bougleux, Gabriel Peyré and Laurent Cohen, Proceedings of Gretsi'09, Sept. 2009.
 Une exploration numérique des performances de l'échantillonage compressé [HAL]
Charles Dossal, Gabriel Peyré and Jalal Fadili, Proceedings of Gretsi'09, Sept. 2009.
 Image Compression with Anisotropic Geodesic Triangulations [HAL]
Sébastien Bougleux, Gabriel Peyré and Laurent Cohen, Proc. ICCV'09, March 2009.
 Challenging Restricted Isometry Constants with Greedy Pursuit [HAL]
Charles Dossal, Gabriel Peyré and Jalal Fadili, Preprint Hal00373450, April 2009.
Links.
 morphologicaldiversity.org:
gather informations related to sparsity and morphological diversity,
to key concepts used by NatImages.
 Numerical Tours:
Matlab experiments to experience modern signal processing. Many of these tours are related
to methods developped by NatImage team members (dictionary learning, block sparsity,
advanced noise model, nonlocal filtering, etc).
 Compressed Sampling at
Rice: gather all the papers on compressive sampling, another key
concept used by NatImages.
 Where
is the Starlets: listing of all the recent fixed and adaptive
sparse representations, one of the two kinds of methods used by NatImages.
 Bandlets:
one of the adaptive representations used by NatImages.
 Grouplets:
one of the adaptive representations used by NatImages.
 Dictionary
learning by B. Olshausen: the first method to learn dictionaries
from data, one of the adaptive representations used by NatImages.
 KSVD:
a recent algorithm for dictionary learning, by M. Elad's team.

