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.

Jean François Aujol (CMLA, ENS Cachan)
Christophe Chesneau (LMNO, Univsersité de Caen)
Laurent Cohen (Universite Paris-Dauphine)
Charles Dossal (IMB, Université Bordeaux 1)
Gabriel Peyré (Université Paris-Dauphine)
Jean-Luc Starck (CEA Saclay).

New book:
Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological Diversity,
Jean-Luc Starck, Fionn Murtagh, Jalal Fadili
Order it online.


The goal of NatImage is to bring both variational-based and sparsity-based 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.

Post-doctoral and Master Students.

  • Gui-Song Xia (supervisors: G. Peyré), Post-doc, 1st April 2011 - 31 Dec. 2011, Gaussian modeling of dynamic textures.
  • Julien Rabin (supervisors: J. Fadili and C. Chesneau), Post-doc, 1st Sept. 2010 - 31 Aout 2011, Local behavior of sparse regularization.
  • Julien Rabin (supervisor: G. Peyré), Post-doc, 1st Novembre 2010 - 31 Aout 2010, Texture modeling with optimal transport.
  • Pierre Maurel (supervisors: J.F. Aujol and G. Peyré), Post-doc, 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), Post-doc, 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.


  • Application to neurosciences: Yves Frégnac (UNIC-CNRS Gif-sur-Yvette)
  • Compressive computations: Laurent Demanet (Stanford)
  • Applications to astrophysics: Jérôme Bobin and Yassir Moudden (CEA Saclay)
  • Non-local energies: Antoni Buades (CNRS)
  • Spatial adaptivity and texture modelling: Yann Gousseau and Vincent Duval (Telecom-Paris Tech)

NatImages Meetings.

    A=Aujol, C=Chesneau, Co=Cohen, D=Dossal, F=Fadili, P=Peyré, S=Starck.

  • Kick-off meeting (talks by all members), 19-20 Janvier 2009, Paris, [All]
  • Working meeting (sparsity and compressed sensing), 11-12 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), 23-26 Juin 2009, Paris, [P,F,D]


  • ICIP'09 (Workshop on sparsity), 7-11 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), 8-11 Sept. 2009, Dijon, [F,P,A,S]
  • Workshop (Geometrical Method in Mathematical Imaging), 9-10 Oct. 2009, Munich, [F,P]
  • Conference (SIAM Conference on Imaging Science), 11-14 Avril 2010, San-Diego, [A,F,P,S]

Journal Publications.

  • Wavelet estimation of the derivatives of an unknown function from a convolution model [HAL]
    Christophe Chesneau,
    Preprint Hal-00399604, 2009.
  • Some first-order algorithms for total variation based image restoration
    Jean-Francois Aujol,
    Journal of Mathematical Imaging and Vision, 34(3), p. 307-327, July 2009.
  • The TVL1 model: a geometric point of view
    V. Duval, Jean-Francois Aujol and Y. Gousseau,
    CMLA Preprint 2009-08, April 2009.
  • Total Variation Projection with First Order Schemes [HAL]
    Jalal Fadili and Gabriel Peyré,
    Preprint Hal-00380491, May 2009.
  • Astronomical Data Analysis and Sparsity: from Wavelets to Compressed Sensing
    Jean-Luc Starck and J. Bobin,
    to appear in Proccedings of the IEEE, 2009.
  • Image decomposition and separation using sparse representations: an overview
    Jalal Fadili, Jean-Luc 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 Gamma-ray Space Telescope
    Jean-Luc Starck , Jalal Fadili, S. Digel , B. Zhang and J. Chiang,
    Astronomy and Astrophysics, in press, 2009.

Conference Publications.


  • 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, non-local 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.
  • K-SVD: a recent algorithm for dictionary learning, by M. Elad's team.