A. Arneodo, E. Bacry, and J. Muzy, Random cascades on wavelet dyadic trees, Journal of Mathematical Physics, vol.39, issue.8, pp.4142-4164, 1998.
DOI : 10.1063/1.532489

F. Bazso, L. Zalanyi, and A. Petroczi, Accuracy of joint entropy and mutual information estimates, 2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No.04CH37541), pp.2843-2846
DOI : 10.1109/IJCNN.2004.1381108

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, pp.65-352, 1993.
DOI : 10.1016/0167-2789(93)90060-E

R. W. Buccigrossi and E. P. Simoncelli, Image compression via joint statistical characterization in the wavelet domain, IEEE Transactions on Image Processing, vol.8, issue.12, pp.1688-1701, 1999.
DOI : 10.1109/83.806616

T. Carleman, Sur leprobì eme des moments, Comptes rendus Acad. Sci. Paris, vol.174, p.1680, 1922.

B. Castaing, The Temperature of Turbulent Flows, Journal de Physique II, vol.6, issue.1, pp.105-114, 1996.
DOI : 10.1051/jp2:1996172
URL : https://hal.archives-ouvertes.fr/jpa-00248278

P. Chainais, Infinitely Divisible Cascades to Model the Statistics of Natural Images, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.29, issue.12, pp.2105-2119, 2007.
DOI : 10.1109/TPAMI.2007.1113

D. Chen, A CONSTRUCTION OF CONVERGENT CASCADE ALGORITHMS IN SOBOLEV SPACES, International Journal of Wavelets, Multiresolution and Information Processing, vol.05, issue.05, pp.685-697, 2007.
DOI : 10.1142/S0219691307001987

A. Chhabra, C. Meneveau, R. Jensen, and K. Sreenivasan, Direct determination of the f(??) singularity spectrum and its application to fully developed turbulence, Physical Review A, vol.40, issue.9, pp.5284-5294, 1989.
DOI : 10.1103/PhysRevA.40.5284

I. Daubechies, Ten lectures on wavelets, CBMS-NSF Series in App, Math, 1992.

J. Delgado, A. Turiel, and N. Parga, Receptive fields of simple cells from a taxonomic study of natural images and suppression of scale redundancy, Neurocomputing, vol.69, issue.10-12, pp.1224-1227, 2006.
DOI : 10.1016/j.neucom.2005.12.081

B. Dubrulle, Intermittency in fully developed turbulence: Log-Poisson statistics and generalized scale covariance, Physical Review Letters, vol.73, issue.7, pp.959-962, 1994.
DOI : 10.1103/PhysRevLett.73.959

U. Frisch, Turbulence: The legacy of A, 1995.

J. Huang and D. Mumford, Statistics of natural images and models, Proc. CVPR, pp.541-547, 1999.

M. Jansen, REFINEMENT INDEPENDENT WAVELETS FOR USE IN ADAPTIVE MULTIRESOLUTION SCHEMES, International Journal of Wavelets, Multiresolution and Information Processing, vol.06, issue.04, pp.521-539, 2008.
DOI : 10.1142/S0219691308002471

B. Lashermes, P. Abry, C. , and P. , NEW INSIGHTS INTO THE ESTIMATION OF SCALING EXPONENTS, International Journal of Wavelets, Multiresolution and Information Processing, vol.02, issue.04, pp.497-523, 2004.
DOI : 10.1142/S0219691304000597

S. Lovejoy, W. Curri, Y. Tessier, M. Claereboudt, E. Bourget et al., Universal multifractals and ocean patchiness: phytoplankton, physical fields and coastal heterogeneity, Journal of Plankton Research, vol.23, issue.2, pp.117-141, 2001.
DOI : 10.1093/plankt/23.2.117

A. B. Mabrouk, STUDY OF SOME NONLINEAR SELF-SIMILAR DISTRIBUTIONS, International Journal of Wavelets, Multiresolution and Information Processing, vol.05, issue.06, pp.907-916, 2007.
DOI : 10.1142/S0219691307002105

S. Mallat, A theory for multiresolution signal decomposition: the wavelet representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.11, issue.7, pp.674-693, 1989.
DOI : 10.1109/34.192463

S. Mallat and S. Zhong, Wavelet transform maxima and multiscale edges, Wavelets and their applications, 1991.

B. Mandelbrot, A. Fisher, C. , and L. , A multifractal model of asset returns, Cowles Foundation Discussion Paper No, p.1164, 1997.

R. Moddemeijer, A statistic to estimate the variance of the histogram-based mutual information estimator based on dependent pairs of observations, Signal Processing, vol.75, issue.1, pp.51-63, 1999.
DOI : 10.1016/S0165-1684(98)00224-2

J. F. Muzy, J. Delour, and E. Bacry, Modelling fluctuations of financial time series: from cascade process to stochastic volatility model, The European Physical Journal B, vol.17, issue.3, pp.17-537, 2000.
DOI : 10.1007/s100510070131

J. Muzy, D. Sornette, J. Delour, and A. Arneodo, Multifractal returns and hierarchical portfolio theory, Quantitative Finance, vol.1, issue.1, pp.131-148, 2001.
DOI : 10.1080/713665541
URL : http://arxiv.org/abs/cond-mat/0008069

E. A. Novikov, Infinitely divisible distributions in turbulence, Physical Review E, vol.50, issue.5, p.3303, 1994.
DOI : 10.1103/PhysRevE.50.R3303

G. Parisi, U. Frisch, M. Ghil, R. Benzi, and G. Parisi, On the singularity structure of fully developedturbulence, in Turbulence and Predictability in Geophysical Fluid Dynamics, Proc. Intl. School of Physics, pp.84-87, 1985.

O. Pont, A. Turiel, and C. Perez-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.388-2025, 2009.
DOI : 10.1016/j.physa.2009.01.041
URL : https://hal.archives-ouvertes.fr/inria-00438521

O. Pont, A. Turiel, and C. J. Pérez-vicente, Description, modelling and forecasting of data with optimal wavelets, Journal of Economic Interaction and Coordination, vol.11, issue.1, pp.39-54, 2009.
DOI : 10.1007/s11403-009-0046-x

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

R. H. Riedi, M. S. Crouse, V. J. Ribeiro, and R. G. Baraniuk, A multifractal wavelet model with application to network traffic, IEEE Transactions on Information Theory, vol.45, issue.3, pp.992-1018, 1999.
DOI : 10.1109/18.761337

S. G. Roux, A. Arneodo, and N. Decoster, A wavelet-based method for multifractal image analysis. III. Applications to high-resolution satellite images of cloud structure, The European Physical Journal B, vol.15, issue.4, pp.765-786, 2000.
DOI : 10.1007/s100510051180

W. Rudin, Real and Complex Analysis, 1987.

D. Sachs, S. Lovejoy, and D. Schertzer, The multifractal scaling of cloud radiances from 1 m to 1 km, Fractals, vol.10, pp.1-12, 2002.

D. Schertzer and S. Lovejoy, Physically based rain and cloud modeling by anisotropic, multiplicative turbulent cascades, Journal of Geophysical Research, vol.92, pp.9692-9714, 1987.

I. Scheuring and R. Riedi, Application of multifractals to the analysis of vegetation pattern, Journal of Vegetation Science, vol.3, issue.4, pp.489-496, 1994.
DOI : 10.2307/3235975

F. Schmitt, D. Schertzer, and S. Lovejoy, MULTIFRACTAL FLUCTUATIONS IN FINANCE, International Journal of Theoretical and Applied Finance, vol.03, issue.03, pp.361-364, 2000.
DOI : 10.1142/S0219024900000206

F. G. Schmitt and P. Chainais, On causal stochastic equations for log-stable multiplicative cascades, The European Physical Journal B, vol.21, issue.2, pp.149-158, 2007.
DOI : 10.1140/epjb/e2007-00205-5
URL : https://hal.archives-ouvertes.fr/hal-00264853

O. Schwartz and E. Simoncelli, Natural signal statistics and sensory gain control, Nature Neuroscience, vol.4, issue.8, pp.819-825, 2001.
DOI : 10.1038/90526

Z. She, Towards a complex system approach for the study of turbulence, Chemical Engineering Science, vol.62, issue.13, pp.3595-3604, 2007.
DOI : 10.1016/j.ces.2006.12.091

Z. S. She and E. Leveque, Universal scaling laws in fully developed turbulence, Physical Review Letters, vol.72, issue.3, pp.336-339, 1994.
DOI : 10.1103/PhysRevLett.72.336

Z. S. She and E. C. Waymire, Quantized Energy Cascade and Log-Poisson Statistics in Fully Developed Turbulence, Physical Review Letters, vol.74, issue.2, pp.262-265, 1995.
DOI : 10.1103/PhysRevLett.74.262

Y. Tessier, S. Lovejoy, and D. Schertzer, Universal Multifractals: Theory and Observations for Rain and Clouds, Journal of Applied Meteorology, vol.32, issue.2, pp.223-250, 1993.
DOI : 10.1175/1520-0450(1993)032<0223:UMTAOF>2.0.CO;2

A. Turiel, J. M. Delgado, and N. Parga, Learning efficient internal representations from natural image collections, Neurocomputing, vol.58, issue.60, pp.60-915, 2004.
DOI : 10.1016/j.neucom.2004.01.146

A. Turiel, J. Isern-fontanet, E. García-ladona, and J. Font, Multifractal Method for the Instantaneous Evaluation of the Stream Function in Geophysical Flows, Physical Review Letters, vol.95, issue.10, p.104502, 2005.
DOI : 10.1103/PhysRevLett.95.104502

A. Turiel, G. Mato, N. Parga, and J. P. Nadal, 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 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 and N. Parga, Multifractal Wavelet Filter of Natural Images, Physical Review Letters, vol.85, issue.15, pp.3325-3328, 2000.
DOI : 10.1103/PhysRevLett.85.3325

A. Turiel and C. Pérez-vicente, Multifractal geometry in stock market time series, Physica A: Statistical Mechanics and its Applications, vol.322, pp.629-649, 2003.
DOI : 10.1016/S0378-4371(02)01830-7
URL : https://hal.archives-ouvertes.fr/inria-00527183

A. Turiel and C. Pérez-vicente, Role of multifractal sources in the analysis of stock market time series, Physica A: Statistical Mechanics and its Applications, vol.355, issue.2-4, pp.475-496, 2005.
DOI : 10.1016/j.physa.2005.04.002

A. Turiel, C. Pérez-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, J. Solé, V. Nieves, J. Ballabrera-poy, and E. García-ladona, Tracking oceanic currents by singularity analysis of Microwave Sea Surface Temperature images, Remote Sensing of Environment, vol.112, issue.5, pp.2246-2260, 2008.
DOI : 10.1016/j.rse.2007.10.007

A. Turiel, H. Yahia, and C. 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, p.15501, 2008.
DOI : 10.1088/1751-8113/41/1/015501
URL : https://hal.archives-ouvertes.fr/hal-00937370

M. J. Wainwright, E. P. Simoncelli, and A. S. Willsky, Random cascades on wavelet trees and their use in analyzing and modeling natural images, Wavelet Applications in Signal and Image Processing VIII, pp.89-123, 2001.
DOI : 10.1117/12.408598