A. Agrawal, R. Raskar, and R. Chellappa, What Is the Range of Surface Reconstructions from a Gradient Field?, pp.86-88, 2006.
DOI : 10.1007/11744023_45

N. Ahuja, A transform for multiscale image segmentation by integrated edge and region detection, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.18, issue.12, pp.1211-1235, 1996.
DOI : 10.1109/34.546258

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media, p.11, 2005.
DOI : 10.1117/3.626196

R. Arsenault, R. Biasi, D. Gallieni, A. Riccardi, N. Hubin et al., A deformable secondary mirror for the VLT, Advances in Adaptive Optics II, pp.6272-6301, 2006.
DOI : 10.1117/12.672879

F. Assémat, R. Wilson, and E. Gendron, Method for simulating infinitely long and non stationary phase screens with optimized memory storage, Optics Express, vol.14, issue.3, pp.988-999, 2006.
DOI : 10.1364/OE.14.000988

J. J. Atick, Could information theory provide an ecological theory of sensory processing?, Network: Computation in Neural Systems, vol.3, issue.2, pp.213-251, 1992.
DOI : 10.1088/0954-898X_3_2_009

M. Azouit and J. Vernin, Optical turbulence profiling with balloons relevant to astronomy and atmospheric physics. Publications of the Astronomical Society of the Pacific, pp.536-543, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00416908

H. W. Babcock, The possibility of compensating astronomical seeing. Publications of the Astronomical Society of the Pacific, p.229, 1953.

L. Baboulaz and P. L. Dragotti, Exact Feature Extraction Using Finite Rate of Innovation Principles With an Application to Image Super-Resolution, IEEE Transactions on Image Processing, vol.18, issue.2, pp.281-298, 2009.
DOI : 10.1109/TIP.2008.2009378

H. Badri, Computer graphics effects from the framework of reconstructible systems. Master's thesis, Rabat faculty of science & INRIA Bordeaux Sud-Ouest, p.126, 2012.

R. G. Baraniuk, E. Candes, M. Elad, and Y. Ma, Applications of Sparse Representation and Compressive Sensing [Scanning the Issue], Proceedings of the IEEE, pp.906-909, 2010.
DOI : 10.1109/JPROC.2010.2047424

R. G. Baraniuk, E. Candes, R. Nowak, and M. Vetterli, Compressive Sampling [From the Guest Editors], IEEE Signal Processing Magazine, vol.25, issue.2, pp.12-13, 2008.
DOI : 10.1109/MSP.2008.915557

R. G. Baraniuk, V. Cevher, M. F. Duarte, and C. Hegde, Modelbased compressive sensing, IEEE Transactions on Information Theory, vol.56, 1982.

J. M. Bardsley, Wavefront Reconstruction Methods for Adaptive Optics Systems on Ground-Based Telescopes, SIAM Journal on Matrix Analysis and Applications, vol.30, issue.1, pp.67-83, 2008.
DOI : 10.1137/06067506X

M. F. Barnsley-]-j and . Beckers, Fractals Everywhere Increasing the size of the isoplanatic patch with multiconjugate adaptive optics. Very Large Telescopes and their Instrumentation, ESO Conference and Workshop Proceedings, pp.43693-703, 1988.

A. Beghi, A. Cenedese, and A. Masiero, Multiscale stochastic approach for phase screens synthesis, Applied Optics, vol.50, issue.21, pp.4124-4133, 2011.
DOI : 10.1364/AO.50.004124

A. J. Bell and T. J. Sejnowski, The ???independent components??? of natural scenes are edge filters, Vision Research, vol.37, issue.23, pp.3327-3338, 1997.
DOI : 10.1016/S0042-6989(97)00121-1

M. and L. Bellac, Des phénomènes critiques aux champs de jauge, une introduction aux méthodes et aux applications de la théorie quantique des champs, InterEditions/Editions du CNRS, collection Savoirs Actuels, 1988.

R. Benzi, L. Biferale, A. Crisanti, G. Paladin, M. Vergassola et al., A random process for the construction of multiaffine fields, Physica D: Nonlinear Phenomena, vol.65, issue.4, p.66, 1993.
DOI : 10.1016/0167-2789(93)90060-E

C. R. Berger, S. Zhou, W. Chen, and P. Willett, Sparse channel estimation for OFDM: Over-complete dictionaries and super-resolution, 2009 IEEE 10th Workshop on Signal Processing Advances in Wireless Communications, 2009.
DOI : 10.1109/SPAWC.2009.5161774

F. Bergholm, Edge Focusing, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.9, issue.6, pp.726-741, 1987.
DOI : 10.1109/TPAMI.1987.4767980

A. Bijaoui, Wavelets and astrophysical applications, Wavelets in Physics, issue.106, 1999.
DOI : 10.1017/CBO9780511613265.006

A. Bijaoui, The wavelet transform: a digital eyepiece to improve our sky vision, Observations & Travaux, vol.70, pp.5-13, 2008.

A. Bijaoui, F. Rué, E. Slezak, and B. Vandame, A multiscale vision model and its applications to astronomical image analysis. Astrophysics and Algorithms: a DIMACS workshop on Massive Astronomical Data Sets, p.106, 1998.

A. Bijaoui, E. Slezak, F. Rué, and E. Lega, Wavelets and the study of the distant Universe, Proceedings of the IEEE, vol.84, issue.4, pp.670-679, 1996.
DOI : 10.1109/5.488706

G. Bofetta, M. Cencini, M. Falcioni, and A. Vulpiani, Predictability: a way to characterize complexity, Physics Reports, vol.356, issue.6, p.75, 2001.
DOI : 10.1016/S0370-1573(01)00025-4

G. Boffetta, M. Cencini, and M. Falcioni, Predictability: a way to characterize complexity, Physics Reports, vol.356, issue.6, pp.367-474, 2002.
DOI : 10.1016/S0370-1573(01)00025-4

P. Bouthemy, A maximum likelihood framework for determining moving edges, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.11, issue.5, pp.499-511, 1989.
DOI : 10.1109/34.24782
URL : https://hal.archives-ouvertes.fr/inria-00075857

C. Boyer, V. Michau, and G. Rousset, Adaptive optics: interaction matrix measurements and real-time control algorithms for the come-on project. Amplitude and Intensity Spatial Interferometry, pp.406-436, 1990.

R. Newbold-bracewell and R. N. Bracewell, The Fourier transform and its applications, p.35, 1986.

R. Newbold-bracewell and A. Riddle, Inversion of Fan-Beam Scans in Radio Astronomy, The Astrophysical Journal, vol.150, pp.427-462, 1967.
DOI : 10.1086/149346

J. Canny, A computational approach to edge detection, IEEE Trans. Pattern Anal. and Mach. Intelligence, vol.8, issue.6, pp.679-698, 1986.

S. Carlsson, Sketch based image coding, Proc. of Premier Colloque Image, pp.71-77, 1984.

S. Carlsson, Sketch based coding of grey level images, Signal Processing, vol.15, issue.1, pp.57-83, 1988.
DOI : 10.1016/0165-1684(88)90028-X

D. C. Chen, S. M. Jones, D. A. Silva, and S. S. Olivier, High-resolution adaptive optics scanning laser ophthalmoscope with dual deformable mirrors, Journal of the Optical Society of America A, vol.24, issue.5, pp.1305-1312, 2007.
DOI : 10.1364/JOSAA.24.001305.m001

J. J. Clark, Singularity theory and phantom edges in scale space, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.10, issue.5, pp.720-727, 1988.
DOI : 10.1109/34.6782

W. Cochran, R. Plemmons, and T. Torgersen, Exploiting Toeplitz structure in atmospheric image restoration, Contemporary Mathematics, vol.280, p.15, 2001.
DOI : 10.1090/conm/280/04628

S. Curtis, S. Shitz, and A. Oppenheim, Reconstruction of nonperiodic two-dimensional signals from zero crossings, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.35, issue.6, pp.890-893, 1987.
DOI : 10.1109/TASSP.1987.1165212

G. M. Dai, Wavefront simulation for atmospheric turbulence, Image Reconstruction and Restoration, vol.62, p.22, 1994.

J. M. Delgado, Filtro optimo para imágenes naturales, aplicación al sistema visual, p.53, 2007.

M. Demerlé, P. Y. Madec, and G. Rousset, Servo-Loop Analysis for Adaptive Optics, Adaptive Optics for Astronomy, pp.73-103, 1994.
DOI : 10.1007/978-94-015-8265-0_5

C. Denker, A. Tritschler, and M. Lofdahl, Image reconstruction. Encyclopedia of Optical Engineering, p.16, 2004.

R. H. Dicke, Phase-contrast detection of telescope seeing errors and their correction, The Astrophysical Journal, vol.198, issue.2, pp.605-615, 1975.
DOI : 10.1086/153639

N. Doble, retinal imaging using adaptive optics and its future role in ophthalmology, Expert Review of Medical Devices, vol.2, issue.2, pp.205-216, 2005.
DOI : 10.1586/17434440.2.2.205

J. H. Elder, Are edges incomplete ? Int, International Journal of Computer Vision, vol.34, issue.2/3, pp.97-122, 1999.
DOI : 10.1023/A:1008183703117

J. H. Elder and S. W. Zucker, Local scale control for edge detection and blur estimation, Proc. European Conf. Computer Vision, pp.57-69, 1996.

J. H. Elder and S. W. Zucker, Local scale control for edge detection and blur estimation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.20, issue.7, pp.699-716, 1998.
DOI : 10.1109/34.689301

B. L. Ellerbroek, First-order performance evaluation of adaptive-optics systems for atmospheric-turbulence compensation in extended-field-of-view astronomical telescopes, Journal of the Optical Society of America A, vol.11, issue.2, pp.783-805, 1994.
DOI : 10.1364/JOSAA.11.000783

B. L. Ellerbroek, Efficient computation of minimum-variance wavefront reconstructors with sparse matrix techniques, J. Opt. Soc. Am. A, vol.19, p.37, 2002.

K. Falconer, Fractal Geometry: Mathematical Foundations and Applications., Biometrics, vol.46, issue.3, p.43, 1990.
DOI : 10.2307/2532125

A. Fannjiang, Exact localization and superresolution with noisy data and random illumination, Inverse Problems, vol.27, issue.6
DOI : 10.1088/0266-5611/27/6/065012

O. Faugeras, Three-dimensional computer vision:a geometric viewpoint, 1993.

P. W. Fieguth and A. S. Willsky, Fractal estimation using models on multiscale trees, IEEE Transactions on Signal Processing, vol.44, issue.5, pp.1297-1300, 1996.
DOI : 10.1109/78.502347

J. C. Fontanella, Wavefront sensing deconvolution and adaptive optics, Journal of Optics, vol.16, issue.6, pp.257-268, 1985.
DOI : 10.1088/0150-536X/16/6/002

D. Fraix-burnet, J. Nieto, and S. Roques, Image deconvolution applied to the 3c 273 jet, Astronomy & Astrophysics, vol.217, pp.387-390, 1989.
URL : https://hal.archives-ouvertes.fr/hal-00002369

D. L. Fried, Optical Resolution Through a Randomly Inhomogeneous Medium for Very Long and Very Short Exposures, Journal of the Optical Society of America, vol.56, issue.10, pp.1372-1379, 1966.
DOI : 10.1364/JOSA.56.001372

D. L. Fried, Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements, Journal of the Optical Society of America, vol.67, issue.3, pp.370-375, 1977.
DOI : 10.1364/JOSA.67.000370

D. L. Fried, Atmospheric Turbulence Optical Effects: Understanding the Adaptive-Optics Implications, pp.25-57, 1993.
DOI : 10.1007/978-94-015-8265-0_2

T. Fusco, Correction partielle et anisoplanétisme en optique adaptative: Traitements a posteriori et optique adaptative multiconjuguée, pp.30-32, 2000.

T. Fusco, J. M. Conan, V. Michau, L. M. Mugnier, and G. Rousset, Efficient phase estimation for large-field-of-view adaptive optics, Optics Letters, vol.24, issue.21, pp.1472-1474, 1999.
DOI : 10.1364/OL.24.001472

T. Fusco, J. M. Conan, V. Michau, G. Rousset, and F. Assemat, Multiconjugate adaptive optics: Comparison of phase reconstruction approaches for large field of view. Atmospheric Propagation, Proc. of SPIE, pp.168-179, 2000.

T. Fusco, J. M. Conan, G. Rousset, L. M. Mugnier, and V. Michau, Optimal wave-front reconstruction strategies for multiconjugate adaptive optics, Journal of the Optical Society of America A, vol.18, issue.10, pp.2527-2538, 2001.
DOI : 10.1364/JOSAA.18.002527

T. Fusco, J. Véran, J. M. Conan, and L. M. Mugnier, Myopic deconvolution method for adaptive optics images of stellar fields, Astronomy and Astrophysics Supplement Series, vol.134, issue.1, pp.193-200, 1999.
DOI : 10.1051/aas:1999133

D. Galun, M. Basri, and A. Brandt, Multiscale Edge Detection and Fiber Enhancement Using Differences of Oriented Means, 2007 IEEE 11th International Conference on Computer Vision, p.70, 2007.
DOI : 10.1109/ICCV.2007.4408920

S. Geman and D. Geman, Stochastic relaxation, gibbs distribution and the bayesian restoration of images, IEEE Trans. Pattern Anal. and Mach. Intelligence, vol.6, issue.6, pp.721-741, 1984.

A. S. Georghiades, P. N. Belhumeur, and D. J. Kriegman, From few to many: illumination cone models for face recognition under variable lighting and pose, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.23, issue.6, pp.643-660, 2001.
DOI : 10.1109/34.927464

L. Gilles, Order-N sparse minimum-variance open-loop reconstructor for extreme adaptive optics, Optics Letters, vol.28, issue.20, pp.1927-1929, 2003.
DOI : 10.1364/OL.28.001927

L. Gilles, C. R. Vogel, and B. L. Ellerbroek, Multigrid preconditioned conjugate-gradient method for large-scale wave-front reconstruction, Journal of the Optical Society of America A, vol.19, issue.9, pp.1817-1822, 2002.
DOI : 10.1364/JOSAA.19.001817

P. Grattoni and A. Guiducci, Contour coding for image description, Pattern Recognition Letters, vol.11, issue.2, pp.95-105, 1990.
DOI : 10.1016/0167-8655(90)90119-M

J. Grazzini, A. Turiel, and H. Yahia, MULTIFRACTAL FORMALISM FOR REMOTE SENSING: A CONTRIBUTION TO THE DESCRIPTION AND THE UNDERSTANDING OF METEOROLOGICAL PHENOMENA IN SATELLITE IMAGES, Complexus Mundi, pp.247-256, 2006.
DOI : 10.1142/9789812774217_0022
URL : https://hal.archives-ouvertes.fr/inria-00422419

J. Grazzini, A. Turiel, H. Yahia, and I. Herlin, Edge-preserving smoothing of high-resolution images with a partial multifractal reconstruction scheme, International Society for Photogrammetry and Remote Sensing (ISPRS), p.126, 2004.
URL : https://hal.archives-ouvertes.fr/inria-00609988

W. E. Grimson, From images to surfaces: A computational study of the human early visual system, p.84, 1981.

A. Habib, J. Vernin, and Z. Benkhaldoun, Application de la technique du SCIDAR g??n??ralis?? aux ??toiles simples, Comptes Rendus Physique, vol.6, issue.3, pp.385-392, 2005.
DOI : 10.1016/j.crhy.2005.02.001

R. M. Haralick, Digital step edges from zero crossing of second directional derivatives, IEEE Trans. Pattern Anal. and Mach. Intelligence, vol.6, issue.1, pp.58-68, 1984.

C. M. Harding, R. A. Johnston, and R. G. Lane, Fast simulation of a kolmogorov phase screen, Applied Optics, vol.38, issue.11, pp.2161-2170, 1999.
DOI : 10.1364/AO.38.002161

J. W. Hardy, Adaptive optics for astronomical telescopes Adaptive optics for astronomical telescopes, p.12, 1998.

J. Hartmann, Bemerkungen über den bau und die justirung von spektrographen, Zt. Instrumentenkd, pp.29-56, 1990.

J. Herrmann, Least-squares wave front errors of minimum norm, Journal of the Optical Society of America, vol.70, issue.1, pp.28-35, 1980.
DOI : 10.1364/JOSA.70.000028

E. Hildreth, Implementation of a theory of edge detection, Massachusetts Inst. Technol, vol.579, issue.1, p.69, 1980.

R. H. Hudgin, Wave-front reconstruction for compensated imaging, Journal of the Optical Society of America, vol.67, issue.3, pp.67-100, 1977.
DOI : 10.1364/JOSA.67.000375

R. Hummel and R. Moniot, Reconstructions from zero crossings in scale space, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.37, issue.12, pp.2111-2130, 1989.
DOI : 10.1109/29.45555

W. and M. Ilhagga, The canny edge detector revisited, Int. J. Comput. Vis, vol.91, pp.251-261, 2011.

W. W. Irving, P. W. Fieguth, and A. S. Willsky, An overlapping tree approach to multiscale stochastic modeling and estimation, IEEE Transactions on Image Processing, vol.6, issue.11, pp.1517-1529, 1997.
DOI : 10.1109/83.641412

W. W. Irving, L. M. Novak, and A. S. Willsky, A multiresolution approach to discrimination in SAR imagery, IEEE Transactions on Aerospace and Electronic Systems, vol.33, issue.4, pp.1157-1169, 1997.
DOI : 10.1109/7.625103

A. Ishimaru, Wavefront Propagation and Scattering in Random Media. Academic, 1978.

G. Rousset, J. Primot, and J. C. Fontanella, Deconvolution from wave front sensing: a new technique for compensating turbulence-degraded images, J. Opt. Soc. Am. A, vol.7, pp.1598-1608, 1990.

P. Jeong and C. I. Kim, Adaptive determination of filter scales for edge detection, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.14, issue.5, pp.579-585, 1992.
DOI : 10.1109/34.134062

M. E. Jernigan and R. W. , Does the eye contain optimal edge detection mechanisms ?, IEEE Trans. Syst, issue.11, pp.441-444, 1981.

M. Kasper, D. P. Looze, S. Hippler, T. Herbst, A. Glindemann et al., Alfa: Adaptive optics for the calar alto observatory optics, control systems, and performance, Experimental Astronomy, vol.10, issue.1, pp.49-73, 2000.
DOI : 10.1023/A:1008165402336

A. K. Katsaggelos, Digital image restoration, Series in Information Information Sciences, p.105, 1991.
DOI : 10.1007/978-3-642-58216-5

V. Khanagha, Novel multiscale methods for nonlinear speech analysis, p.46, 2013.
URL : https://hal.archives-ouvertes.fr/tel-00821896

V. Khanagha and K. Daoudi, Efficient multipulse approximation of speech excitation using the most singular manifold, IEEE Interspeech, issue.6, p.126
URL : https://hal.archives-ouvertes.fr/hal-00684895

V. Khanagha, K. Daoudi, O. Pont, H. Yahia, and A. Turiel, Improving text-independent phonetic segmentation based on the Microcanonical Multiscale Formalism, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), p.126, 2011.
DOI : 10.1109/ICASSP.2011.5947350
URL : https://hal.archives-ouvertes.fr/inria-00557661

V. Khanagha, K. Daoudi, O. Pont, H. Yahia, and A. Turiel, Nonlinear speech representation based on local predictability exponents, Neurocomputing Journal, p.126, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00685019

R. Kimmel and A. M. Bruckstein, Regularized laplacian zero crossings as optimal edge integrators, International Journal of Computer Vision, vol.53, issue.3, pp.225-243, 2003.
DOI : 10.1023/A:1023030907417

V. A. Korkiakoski, Improving the performance of adaptive optics systems with optimized control methods, 2008.

P. Kovesi, Image features from phase congruency, Journal of Computer Vision Research, p.71, 1999.

A. Labeyrie, Attainment of diffraction limited resolution in large telescopes by fourier analysing speckle patterns in star images, Astronomy and Astrophysics, vol.6, pp.85-103, 1970.

O. Laligant and F. Truchetet, A Nonlinear Derivative Scheme Applied to Edge Detection, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.32, issue.2, pp.242-257, 2010.
DOI : 10.1109/TPAMI.2008.282
URL : https://hal.archives-ouvertes.fr/hal-00582610

R. G. Lane, A. Glindemann, and J. C. Dainty, Simulation of a Kolmogorov phase screen, Waves in Random Media, pp.209-224, 1992.
DOI : 10.1088/0959-7174/2/3/003

A. Lesne, Méthodes de renormalisation, Eyrolles Science, p.70, 1995.

W. Y. Leung, Inverse problems in astronomical and general imaging, pp.35-116, 2002.

F. Levet and X. Granier, Improved skeleton extraction and surface generation for sketch-based modeling, Proceedings of Graphics Interface 2007 on , GI '07, p.69, 2007.
DOI : 10.1145/1268517.1268524
URL : https://hal.archives-ouvertes.fr/inria-00187161

S. Z. Li, Close-form solution and parameter selection for convex minimization-based edge-preserving smoothing, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.20, issue.9, pp.916-932, 1998.
DOI : 10.1109/34.713359

P. Liang and Y. W. Wang, Local scaled controlled anisotropic diffusion with local noise estimate for image smoothing and edge detection, Sixth International Conference on Computer Vision (ICCV), p.70, 1998.

T. Lindeberg, Scale-Space Theory in Computer Vision, 1994.
DOI : 10.1007/978-1-4757-6465-9

T. Lindeberg, Edge detection and ridge detection with automatic scale selection, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.117-154, 1998.
DOI : 10.1109/CVPR.1996.517113

T. Lindeberg and . Ter-haar-romeny, Linear scale-space: (I) Basic theory and (II) Early visual operations, Geometry-Driven Diffusion, p.77, 1994.

H. K. Liu, Two- and three-dimensional boundary detection, Computer Graphics and Image Processing, vol.6, issue.2, pp.123-134, 1977.
DOI : 10.1016/S0146-664X(77)80008-7

B. F. Logan, Information in the Zero Crossings of Bandpass Signals, Bell System Technical Journal, vol.56, issue.4, pp.487-510
DOI : 10.1002/j.1538-7305.1977.tb00522.x

S. Lovejoy and D. Schertzer, Multifractals, universality classes and satellite and radar measurements of cloud and rain fields, Journal of Geophysical Research, vol.92, issue.D3, pp.2021-2034, 1990.
DOI : 10.1029/JD095iD03p02021

W. H. Lunscher, The Asymptotic Optimal Frequency Domain Filter for Edge Detection, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.5, issue.6, pp.678-680, 1983.
DOI : 10.1109/TPAMI.1983.4767462

W. H. Lunscher and M. P. Beddoes, Optimal Edge Detector Design I: Parameter Selection and Noise Effects, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.8, issue.2, pp.164-177, 1986.
DOI : 10.1109/TPAMI.1986.4767770

P. Y. Madec, Control techniques, in Adaptive Optics in Astronomy, p.30, 1999.

P. Y. Maeda, Zernike polynomials and their use in describing the wavefront aberrations of the human eye, 2003.

S. K. Maji, O. Pont, H. Yahia, and J. Sudre, Inferring Information Across Scales in Acquired Complex Signals, European Conf. Complex Systems, pp.2012-2018
DOI : 10.1007/978-3-319-00395-5_31
URL : https://hal.archives-ouvertes.fr/hal-00872371

S. K. Maji, H. Yahia, and H. Badri, Reconstructing an image from its edge representation, Digital Signal Processing, vol.23, issue.6, p.54, 2013.
DOI : 10.1016/j.dsp.2013.06.013
URL : https://hal.archives-ouvertes.fr/hal-00850398

S. K. Maji, H. Yahia, O. Pont, T. Fusco, V. Michau et al., A multiscale approach to phase reconstruction for Adaptive Optics, 2011 10th International Workshop on Electronics, Control, Measurement and Signals, p.106, 2011.
DOI : 10.1109/IWECMS.2011.5952381
URL : https://hal.archives-ouvertes.fr/inria-00591097

S. K. Maji, H. Yahia, O. Pont, J. Sudre, T. Fusco et al., Towards multiscale reconstruction of perturbated phase from hartmannshack acquisitions, IEEE AHS, p.106
URL : https://hal.archives-ouvertes.fr/hal-00703723

S. Mallat, A wavelet tour of signal processing, pp.59-77, 1999.

S. Mallat and W. L. Hwang, Singularity detection and processing with wavelets, IEEE Transactions on Information Theory, vol.38, issue.2, pp.617-643, 1992.
DOI : 10.1109/18.119727
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.36.5153

S. Mallat and S. Zhong, Characterization of signals from multiscale edges, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.14, issue.7, pp.710-732, 1992.
DOI : 10.1109/34.142909

D. H. Marimont and Y. Rubner, A probabilistic framework for edge detection and scale selection, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271), p.70, 1998.
DOI : 10.1109/ICCV.1998.710720

D. Marr and E. Hildreth, Theory of Edge Detection, Proceedings of the Royal Society B: Biological Sciences, vol.207, issue.1167, pp.187-217, 1980.
DOI : 10.1098/rspb.1980.0020

B. L. Mcglamery, Computer simulation studies of compensation of turbulence degraded images, Image Processing, pp.225-223, 1976.

D. G. Morgenthaler and A. Rosenfeld, Multidimensional Edge Detection by Hypersurface Fitting, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.3, issue.4, pp.482-486, 1981.
DOI : 10.1109/TPAMI.1981.4767134

M. C. Morrone and D. C. Burr, Feature Detection in Human Vision: A Phase-Dependent Energy Model, Proceedings of the Royal Society B: Biological Sciences, vol.235, issue.1280, p.71, 1988.
DOI : 10.1098/rspb.1988.0073

L. Mugnier, G. L. Besnerais, and S. Meimon, Inversion in optical imaging through atmospheric turbulence in Bayesian approach to inverse problems, Jérôme Idier ed. ISTE, vol.28, issue.35, pp.34-105, 2008.

L. M. Mugnier, C. Robert, J. Conan, V. Michau, and S. Salem, Myopic deconvolution from wavefront sensing, p.106
DOI : 10.1364/josaa.18.000862

L. M. Mugnier, C. Robert, J. Conan, V. Michau, and S. Salem, Regularized multiframe myopic deconvolution from wavefront sensing, Proc. SPIE 3763, Propagation and Imaging through the Atmosphere III, p.17, 1999.
DOI : 10.1117/12.363607

S. Muraki, N. Yokoya, and K. Yamamoto, Surface reconstruction from a contour line image by regularization, Systems and Computers in Japan, vol.30, issue.11, pp.81-91, 1992.
DOI : 10.1002/scj.4690230207

T. Nakajima, Signal-to-noise ratio of the bispectral analysis of speckle interferometry, Journal of the Optical Society of America A, vol.5, issue.9, pp.1477-1491, 1988.
DOI : 10.1364/JOSAA.5.001477

V. S. Nalwa and T. O. Binford, On Detecting Edges, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.8, issue.6, pp.699-714, 1986.
DOI : 10.1109/TPAMI.1986.4767852

R. J. Noll, Zernike polynomials and atmospheric turbulence*, Journal of the Optical Society of America, vol.66, issue.3, pp.207-211, 1976.
DOI : 10.1364/JOSA.66.000207

R. J. Noll, Phase estimates from slope-type wave-front sensors, Journal of the Optical Society of America, vol.68, issue.1, pp.139-140, 1978.
DOI : 10.1364/JOSA.68.000139

A. M. Obukhov, The structure of the temperature field in a turbulent flow, Izv. Akad. Nauk. SSSR, Ser. Geogr. and Geophys, vol.13, issue.11, pp.58-69, 1949.

R. Pacanowski, X. Granier, C. Schlick, and P. Poulin, Sketch and paint-based interface for highlight modeling, Eurographics Workshop on Sketch-Based Interfaces and Modeling, p.69, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00277102

G. Parisi and U. Frisch, On the singularity structure of fully developed turbulence turbulence and predictability in geophysical fluid dynamics

P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.12, issue.7, pp.629-639, 1990.
DOI : 10.1109/34.56205

J. A. Perreault, T. G. Bifano, B. M. Levine, and M. N. Horenstein, Adaptive optic correction using microelectromechanical deformable mirrors, Optical Engineering, vol.41, pp.561-566, 2002.

I. Pitas and A. N. Venetsalopoulous, Edge Detectors Based on Nonlinear Filters, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.8, issue.4, pp.538-550, 1986.
DOI : 10.1109/TPAMI.1986.4767819

O. Pont, Universality in multiscale, turbulent-like self-organization: from algal blooms to heartbeat to stock market dynamics, IFISC, vol.41, p.126, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00533395

O. Pont, A. Turiel, and C. Perez-vicente, ON OPTIMAL WAVELET BASES FOR THE REALIZATION OF MICROCANONICAL CASCADE PROCESSES, International Journal of Wavelets, Multiresolution and Information Processing, vol.09, issue.01, pp.35-61, 2011.
DOI : 10.1142/S0219691311003943
URL : https://hal.archives-ouvertes.fr/inria-00582372

O. Pont, A. Turiel, and C. J. Pérez-vicente, Application of the microcanonical multifractal formalism to monofractal systems, Physical Review E, vol.74, issue.6, pp.61110-061123, 2006.
DOI : 10.1103/PhysRevE.74.061110
URL : https://hal.archives-ouvertes.fr/inria-00438520

O. Pont, A. Turiel, and C. J. Pérez-vicente, Empirical evidences of a common multifractal signature in economic, biological and physical systems, Physica A: Statistical Mechanics and its Applications, vol.388, issue.10, pp.2025-2035, 2009.
DOI : 10.1016/j.physa.2009.01.041
URL : https://hal.archives-ouvertes.fr/inria-00438521

O. Pont, A. Turiel, and H. Yahia, An Optimized Algorithm for the Evaluation of Local Singularity Exponents in Digital Signals, 14th International Workshop on Combinatorial Image Analysis (IWCIA 2011), LNCS 6636, p.75, 2011.
DOI : 10.1088/1751-8113/41/1/015501
URL : https://hal.archives-ouvertes.fr/inria-00581057

C. Pottier, Combinaison multi-capteurs de données de couleur de l'eau : Application en océanographie opérationnelle, 2006.

C. Pottier, A. Turiel, and V. Garçon, Inferring missing data in satellite chlorophyll maps using turbulent cascading, Remote Sensing of Environment, vol.112, issue.12, pp.4242-4260, 2008.
DOI : 10.1016/j.rse.2008.07.010
URL : https://hal.archives-ouvertes.fr/hal-00402483

F. Quiros-pacheco, Reconstruction and control laws for multiconjugate adaptive optics in astronomy, p.27, 2007.

A. Riccardi, G. Brusa, M. Xompero, D. Zannoti, C. D. Vecchio et al., The adaptive secondary mirrors for the Large Binocular Telescope: a progress report, Advancements in Adaptive Optics, pp.1564-1571, 2004.
DOI : 10.1117/12.551578

F. Rigaut, Ground conjugate wide field adaptive optics for the elts, ESO Conf. Beyond conventional adaptive optics, pp.11-16, 2002.

F. Rigaut, G. Rousset, P. Kern, J. C. Fontanella, J. P. Gaffard et al., Adaptive optics on a 3.6-m telescope -results and performance, Astronomy and Astrophysics, vol.250, pp.280-290, 1991.

F. Roddier, V The Effects of Atmospheric Turbulence in Optical Astronomy, Progress in Optics, pp.283-376, 1981.
DOI : 10.1016/S0079-6638(08)70204-X

F. Roddier, Curvature sensing and compensation: a new concept in adaptive optics, Applied Optics, vol.27, issue.7, pp.1223-1225, 1988.
DOI : 10.1364/AO.27.001223

F. Roddier and U. K. , Adaptive optics in astronomy, pp.35-36, 1999.

N. Roddier, Atmospheric wavefront simulation using Zernike polynomials, Optical Engineering, vol.29, issue.10, pp.1174-1180, 1921.
DOI : 10.1117/12.55712

G. Rodrigues, Adaptive optics with segmented deformable bimorph mirrors, p.33, 2010.

M. C. Roggemann and B. M. Welsh, Imaging Through Turbulence, p.22, 1996.

S. Roques, F. Bourzeix, and K. Bouyoucef, Soft-thresholding technique and restoration of 3C273 jet, Astrophysics and Space Science, vol.41, issue.7, pp.297-304, 1996.
DOI : 10.1007/BF00645783

S. Roques, B. Serre, and N. Dolez, Band-limited interpolation applied to the time series of rapidly oscillating stars, Monthly Notices of the Royal Astronomical Society, vol.308, issue.3, pp.876-886, 1999.
DOI : 10.1046/j.1365-8711.1999.02776.x

G. Rousset, Wave-front sensing, Adaptive Optics in Astronomy, F. Roddier, p.29, 1999.

G. Rousset and J. Beuzit, The COME-ONE/ADONIS systems, Adaptive Optics in Astronomy, F. Roddier, 1999.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron et al., Design of the nasmyth adaptive optics system (naos) of the vlt, astronomical telescopes and instrumentation, Proc. Soc. Photo- Opt. Instrum. Eng, vol.3353, p.28, 1998.

F. Rué and A. Bijaoui, Pyramidal vision model applied to astronomical images, Wavelet Applications in Signal and Image Processing IV, Proc. SPIE, pp.373-383, 1996.

R. A. Salinas, C. Richardson, M. A. Abidi, and R. C. Gonzalez, Data fusion: color edge detection and surface reconstruction through regularization, IEEE Transactions on Industrial Electronics, vol.43, issue.3, pp.355-363, 1996.
DOI : 10.1109/41.499807

P. Sarkar and K. L. Boyer, On optimal infinite impulse response edge detection filters, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.13, issue.11, pp.1154-1171, 1991.
DOI : 10.1109/34.103275

R. J. Sasiela and J. G. Mooney, An Optical Phase Reconstructor Based On Using A Multiplier-Accumulator Approach, Adaptive Optics, pp.170-176, 1985.
DOI : 10.1117/12.949018

D. Schleicher, Hausdorff dimension, its properties, and its surprises, American Mathematical Monthly, vol.114, pp.509-528, 2007.

J. D. Schmidt, Free-space optical communications performance enhancement by use of a single adaptive optics correcting element, 2006.

C. Schwartz, G. Baum, and E. N. Ribak, Turbulence-degraded wave fronts as fractal surfaces, Journal of the Optical Society of America A, vol.11, issue.1, pp.444-451, 1994.
DOI : 10.1364/JOSAA.11.000444

M. Séchaud, Wave-front compensation devices, in Adaptive Optics in Astronomy, p.27, 1999.

G. Sedmak, Implementation of fast-Fourier-transform-based simulations of extra-large atmospheric phase and scintillation screens, Applied Optics, vol.43, issue.23, pp.4527-4538, 2004.
DOI : 10.1364/AO.43.004527

R. Shack, Production and use of a lenticular hartmann screen, J. Opt. Soc. Am. A, pp.61-88, 1971.

K. S. Shanmugham, F. M. Dickey, and J. A. Green, An Optimal Frequency Domain Filter for Edge Detection in Digital Pictures, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.1, issue.1, pp.37-49, 1979.
DOI : 10.1109/TPAMI.1979.4766874

Z. S. She and E. Leveque, Universal scaling laws in fully developed turbulence, Physical Review Letters, vol.72, issue.3, pp.336-345, 1994.
DOI : 10.1103/PhysRevLett.72.336

W. H. Southwell, Wave-front estimation from wave-front slope measurements, Journal of the Optical Society of America, vol.70, issue.8, pp.998-1006, 1980.
DOI : 10.1364/JOSA.70.000998

H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena, 1971.
DOI : 10.1063/1.3127900

J. Starck, F. Murthag, and J. M. Fadili, Sparse Image and Signal Processing: wavelets, curvelets, morphological diversity, p.106, 2010.
DOI : 10.1017/CBO9780511730344
URL : https://hal.archives-ouvertes.fr/hal-01132685

K. Suzuki, I. Oriba, and N. Sugie, Neural edge enhancer for supervised edge enhancement from noisy images, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.25, issue.12, pp.1582-1596, 2003.
DOI : 10.1109/TPAMI.2003.1251151

A. J. Tabatabai and R. Mitchell, Edge Location to Subpixel Values in Digital Imagery, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.6, issue.2, pp.188-201, 1984.
DOI : 10.1109/TPAMI.1984.4767502

V. Y. Tan, A. Anandkumar, L. Tong, and A. S. Willsky, A Large-Deviation Analysis of the Maximum-Likelihood Learning of Markov Tree Structures, IEEE Transactions on Information Theory, vol.57, issue.3, pp.1714-1735, 2011.
DOI : 10.1109/TIT.2011.2104513

H. Tennekes and J. L. Lumley, A first course in turbulence, 1972.

A. Tokovinin, Cfio overview of adaptive optics, p.32

A. Tokovinin, Seeing improvement with ground-layer adaptive optics. Publications of the Astronomical Society of the Pacific, pp.941-951, 2004.

V. Torre and T. A. Poggio, On Edge Detection, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.8, issue.2, pp.147-163, 1986.
DOI : 10.1109/TPAMI.1986.4767769

Y. Traonmilin, S. Ladjal, and A. Almansa, Quantification de la robustesse de la super-résolution par minimisation l1, GRETSI, issue.1, 2013.

A. Turiel and A. Pozo, Reconstructing images from their most singular fractal manifold, IEEE Transactions on Image Processing, vol.11, issue.4, pp.345-350, 2002.
DOI : 10.1109/TIP.2002.999668
URL : https://hal.archives-ouvertes.fr/inria-00532760

A. Turiel, J. M. Delgado, and N. Parga, Learning efficient internal representations from natural image collections, Neurocomputing, vol.58, issue.60, pp.58-60915, 2004.
DOI : 10.1016/j.neucom.2004.01.146

A. Turiel, G. Mato, N. Parga, and J. P. , Self-Similarity Properties of Natural Images Resemble Those of Turbulent Flows, Physical Review Letters, vol.80, issue.5, pp.1098-1101, 1998.
DOI : 10.1103/PhysRevLett.80.1098
URL : https://hal.archives-ouvertes.fr/hal-00143846

A. Turiel, J. Nadal, and N. Parga, Orientational minimal redundancy wavelets: from edge detection to perception, Vision Research, vol.43, issue.9, pp.1061-1079, 2003.
DOI : 10.1016/S0042-6989(03)00012-9
URL : https://hal.archives-ouvertes.fr/inria-00527185

A. Turiel and N. Parga, The Multifractal Structure of Contrast Changes in Natural Images: From Sharp Edges to Textures, Neural Computation, vol.12, issue.4, pp.763-793, 2000.
DOI : 10.1098/rspb.1998.0303

A. Turiel, C. J. Pérz-vicente, and J. Grazzini, Numerical methods for the estimation of multifractal singularity spectra on sampled data: A comparative study, Journal of Computational Physics, vol.216, issue.1, pp.362-390, 2006.
DOI : 10.1016/j.jcp.2005.12.004

A. Turiel, H. Yahia, and C. J. Pérez-vicente, Microcanonical multifractal formalism???a geometrical approach to multifractal systems: Part I. Singularity analysis, Journal of Physics A: Mathematical and Theoretical, vol.41, issue.1, pp.50-72, 2008.
DOI : 10.1088/1751-8113/41/1/015501
URL : https://hal.archives-ouvertes.fr/hal-00937370

J. Vallerga, J. Mcphate, A. Tremsin, O. Siegmund, B. Mikulec et al., Optically sensitive medipix2 detector for adaptive optics wavefront sensing. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, pp.263-269, 2005.

J. H. Van-hateren, Theoretical predictions of spatiotemporal receptive fields of fly LMCs, and experimental validation, Journal of Comparative Physiology A, vol.171, issue.2, pp.157-170, 1992.
DOI : 10.1007/BF00188924

J. H. Van-hateren, A. Van, and . Schaaf, Independent component filters of natural images compared with simple cells in primary visual cortex, Proc.R. Soc. Lond., B265. 69, p.90, 1998.
DOI : 10.1098/rspb.1998.0303

J. Vernin, R. Barletti, G. Ceppatelli, L. Paterno, A. Righini et al., Optical remote sensing of atmospheric turbulence: a comparison with simultaneous thermal measurements, Applied Optics, vol.18, issue.2, pp.243-247, 1979.
DOI : 10.1364/AO.18.000243

S. J. Wang and T. O. Binford, Generic, model-based estimation and detection of discontinuities in image surfaces, Proceedings of 1994 ARPA Image Understanding Workshop, pp.1443-1449, 1994.

X. Wang, Laplacian Operator-Based Edge Detectors, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.29, issue.5, pp.886-890, 2007.
DOI : 10.1109/TPAMI.2007.1027

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, Image Quality Assessment: From Error Visibility to Structural Similarity, IEEE Transactions on Image Processing, vol.13, issue.4, pp.600-612, 2004.
DOI : 10.1109/TIP.2003.819861

Z. Wang and E. P. Simoncelli, Local phase coherence and the perception of blur, Adv. Neural Inf. Process. Syst, vol.16, p.71, 2004.

J. Weickert, Anisotropic diffusion in image processing, p.87, 2006.

H. Wendt and P. Abry, Multifractality Tests Using Bootstrapped Wavelet Leaders, IEEE Transactions on Signal Processing, vol.55, issue.10, 2007.
DOI : 10.1109/TSP.2007.896269
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.646.5436

R. W. Wilson, SLODAR: measuring optical turbulence altitude with a Shack-Hartmann wavefront sensor, Monthly Notices of the Royal Astronomical Society, vol.337, issue.1, pp.103-108, 2002.
DOI : 10.1046/j.1365-8711.2002.05847.x

A. Witkin, SCALE-SPACE FILTERING, Proc. IJCAI, p.70, 1983.
DOI : 10.1016/B978-0-08-051581-6.50036-2

H. Yahia, J. Sudre, V. Garçon, and C. Pottier, High-resolution ocean dynamics from microcanonical formulations in non linear complex signal analysis, AGU FALL MEETING, p.126, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00650224

H. Yahia, J. Sudre, C. Pottier, and V. Garçon, Motion analysis in oceanographic satellite images using multiscale methods and the energy cascade, Pattern Recognition, vol.43, issue.10, pp.3591-3604, 2010.
DOI : 10.1016/j.patcog.2010.04.011
URL : https://hal.archives-ouvertes.fr/inria-00423748

A. Yuille and T. Poggio, Fingerprints theorems for zero crossings, Journal of the Optical Society of America A, vol.2, issue.5, pp.683-692, 1985.
DOI : 10.1364/JOSAA.2.000683

A. L. Yuille and T. A. Poggio, Scaling Theorems for Zero Crossings, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.8, issue.1, pp.15-25, 1986.
DOI : 10.1109/TPAMI.1986.4767748

F. Zamkotsian, H. Camon, N. Fabre, V. Conedera, and G. Moreaux, Micro-deformable mirror for next-generation adaptive optical systems, Adaptive Optical System Technologies II
DOI : 10.1117/12.458845

Y. Zeevi and D. Rotem, Image reconstruction from zero crossings, IEEE Trans. Acoust., Speech, Signal Processing, vol.34, pp.1269-1277, 1986.

X. X. Zhu and R. Bamler, Super-resolution for 4-d sar tomography via compressive sensing, 8th European Conference on Synthetic Aperture Radar, 2010.

S. W. Zucker and R. A. Hummel, A Three-Dimensional Edge Operator, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.3, issue.3, pp.324-331, 1981.
DOI : 10.1109/TPAMI.1981.4767105