J. G. Daugman, Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters, Journal of the Optical Society of America A, vol.2, issue.7, pp.1160-1169, 1985.
DOI : 10.1364/JOSAA.2.001160

R. L. De-valois, D. G. Albrecht, and L. G. , Spatial frequency selectivity of cells in macaque visual cortex, Vision Research, vol.22, issue.5, pp.545-559, 1982.
DOI : 10.1016/0042-6989(82)90113-4

E. C. Hildreth, Implementation of a theory of edge detection, 1980.

D. Marr and T. Poggio, A Computational Theory of Human Stereo Vision, Proceedings of the Royal Society B: Biological Sciences, vol.204, issue.1156, pp.301-328, 1156.
DOI : 10.1098/rspb.1979.0029

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

P. Massopust, Fractal Functions, Fractal Surfaces, and Wavelets, 1994.

B. A. Olshausen and D. J. Field, Sparse coding with an overcomplete basis set: A strategy employed by V1?, Vision Research, vol.37, issue.23, pp.3311-3325, 1997.
DOI : 10.1016/S0042-6989(97)00169-7

J. M. Shapiro, Embedded image coding using zerotrees of wavelet coefficients, IEEE Transactions on Signal Processing, vol.41, issue.12, pp.3445-3462, 1993.
DOI : 10.1109/78.258085

G. Davis and A. Nosratinia, Wavelet-Based Image Coding: An Overview, Applied and Computational Control, Signals, and Circuits, pp.369-434, 1998.
DOI : 10.1007/978-1-4612-0571-5_8

Y. Meyer, Oscillating patterns in image processing and nonlinear evolution equations, The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures, 2001.
DOI : 10.1090/ulect/022

J. Aujol, G. Aubert, L. Blanc-feraud, and A. Chambolle, Image Decomposition into a Bounded Variation Component and an Oscillating Component, Journal of Mathematical Imaging and Vision, vol.15, issue.3, pp.71-88, 2005.
DOI : 10.1007/s10851-005-4783-8

URL : https://hal.archives-ouvertes.fr/hal-00202001

]. L. Duval, WITS: Where Is The Star let? http

J. Daugman, Two-dimensional spectral analysis of cortical receptive field profiles, Vision Research, vol.20, issue.10, pp.847-856, 1980.
DOI : 10.1016/0042-6989(80)90065-6

E. J. Candès and D. L. Donoho, Curvelets ? a surprisingly effective nonadaptive representation for objects with edges, Curves and Surfaces, pp.105-120, 1999.

R. Rubinstein, A. M. Bruckstein, and M. Elad, Dictionaries for Sparse Representation Modeling, Proc. IEEE, pp.1045-1057, 2010.
DOI : 10.1109/JPROC.2010.2040551

URL : https://hal.archives-ouvertes.fr/inria-00565811

J. Romberg, Multiscale geometric image processing, 2003.

A. Lisowska, Geometrical wavelets and their generalizations in digital image coding and processing, 2005.

H. Führ, L. Demaret, and F. Friedrich, Beyond wavelets: New image representation paradigms, Document and Image Compression, 2006.

J. Ma and G. Plonka, The Curvelet Transform, IEEE Signal Processing Magazine, vol.27, issue.2, pp.118-133, 2010.
DOI : 10.1109/MSP.2009.935453

URL : https://hal.archives-ouvertes.fr/hal-00557892

J. M. Fadili and J. Starck, Curvelets and ridgelets, Encyclopedia of Complexity and Systems Science, pp.1718-1738, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00256318

J. Starck, F. Murtagh, and J. M. Fadili, Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological Diversity, 2010.
DOI : 10.1017/CBO9780511730344

URL : https://hal.archives-ouvertes.fr/hal-01132685

K. Szatmáry and J. Vinkó, Periodicities of the light curve of the semiregular variable star Y Lyncis, Monthly Notices of the Royal Astronomical Society, vol.256, issue.2, pp.321-328, 1992.
DOI : 10.1093/mnras/256.2.321

L. Jacques, L. Duval, C. Chaux, and G. Peyré, Addendum to " A panorama on multiscale geometric representations, intertwining spatial, directional and frequency selectivity, 2011.

A. Haar, Zur Theorie der orthogonalen Funktionensysteme, Mathematische Annalen, vol.6, issue.3, pp.331-371, 1910.
DOI : 10.1007/BF01456326

URL : https://hal.archives-ouvertes.fr/hal-01333722

O. Christensen, Frames, Riesz bases, and discrete Gabor/wavelet expansions, Bulletin of the American Mathematical Society, vol.38, issue.03, pp.273-291, 2001.
DOI : 10.1090/S0273-0979-01-00903-X

R. Duffin and A. Schaeffer, A class of nonharmonic Fourier series, Transactions of the American Mathematical Society, vol.72, issue.2, pp.341-366, 1952.
DOI : 10.1090/S0002-9947-1952-0047179-6

P. G. Casazza, The art of frame theory, Taiwanese J. of Math, vol.15, issue.4, pp.129-201, 2000.

J. Kova?evi´kova?evi´c and A. Chebira, Life beyond bases: The advent of frames (part I), IEEE Signal Process. Mag, pp.86-104, 2007.

J. Kova?evi´kova?evi´c and A. Chebira, Life beyond bases: The advent of frames (part II), IEEE Signal Process. Mag, pp.115-125, 2007.

S. Mallat, A wavelet tour of signal processing: the sparse way, 2009.

R. N. Bracewell, The Fourier Transform and Its Applications, American Journal of Physics, vol.34, issue.8, 1986.
DOI : 10.1119/1.1973431

P. Brémaud, Mathematical principles of signal processing: Fourier and wavelet analysis, 2002.
DOI : 10.1007/978-1-4757-3669-4

J. Allen, Short term spectral analysis, synthesis, and modification by discrete Fourier transform, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.25, issue.3, pp.235-238, 1977.
DOI : 10.1109/TASSP.1977.1162950

R. Wilson, A. D. Calway, and E. R. Pearson, A generalized wavelet transform for Fourier analysis: the multiresolution Fourier transform and its application to image and audio signal analysis, IEEE Transactions on Information Theory, vol.38, issue.2, pp.674-690, 1992.
DOI : 10.1109/18.119730

A. P. Witkin, Scale-space filtering: A new approach to multi-scale description, ICASSP '84. IEEE International Conference on Acoustics, Speech, and Signal Processing, pp.150-153, 1984.
DOI : 10.1109/ICASSP.1984.1172729

J. Babaud, A. P. Witkin, M. Baudin, and R. O. Duda, Uniqueness of the Gaussian Kernel for Scale-Space Filtering, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.8, issue.1, pp.26-33, 1986.
DOI : 10.1109/TPAMI.1986.4767749

K. Bredies, D. A. Lorenz, and P. Maass, Mathematical concepts of multiscale smoothing, Applied and Computational Harmonic Analysis, vol.19, issue.2, pp.141-161, 2005.
DOI : 10.1016/j.acha.2005.02.007

T. Lindeberg, Discrete derivative approximations with scale-space properties: A basis for low-level feature extraction, Journal of Mathematical Imaging and Vision, vol.9, issue.4, pp.349-379, 1993.
DOI : 10.1007/BF01664794

L. Florack and A. Kuijper, The topological structure of scale-space images, 1998.

P. J. Burt and E. H. Adelson, The Laplacian Pyramid as a Compact Image Code, IEEE Transactions on Communications, vol.31, issue.4, pp.532-540, 1983.
DOI : 10.1109/TCOM.1983.1095851

S. Treitel and J. L. Shanks, The Design of Multistage Separable Planar Filters, IEEE Transactions on Geoscience Electronics, vol.9, issue.1, pp.106-133, 1971.
DOI : 10.1109/TGE.1971.271457

R. Deriche, Recursively implementing the Gaussian and its derivative, 1993.

R. Manduchi, P. Perona, and D. Shy, Efficient deformable filter banks, IEEE Transactions on Signal Processing, vol.46, issue.4, pp.1168-1173, 1998.
DOI : 10.1109/78.668570

E. H. Adelson, C. H. Anderson, J. R. Bergen, P. J. Burt, and J. M. Ogden, Pyramid method in image processing, RCA Eng, vol.29, issue.6, pp.33-41, 1984.

J. M. Ogden, E. H. Adelson, J. R. Bergen, and P. J. Burt, Pyramid-based computer graphics, RCA Eng, vol.30, issue.5, pp.4-15, 1985.

M. N. Do and M. Vetterli, Framing pyramids, IEEE Transactions on Signal Processing, vol.51, issue.9, pp.2329-2342, 2003.
DOI : 10.1109/TSP.2003.815389

J. Weickert, S. Ishikawa, and A. Imiya, Scale-space has been discovered in Japan, 1997.

T. Lindeberg, Generalized Gaussian Scale-Space Axiomatics Comprising Linear Scale-Space, Affine Scale-Space and Spatio-Temporal Scale-Space, Journal of Mathematical Imaging and Vision, vol.35, issue.3, 4, pp.36-81, 2011.
DOI : 10.1007/s10851-010-0242-2

A. Grossman and J. Morlet, Decompositions of functions into wavelets of constant shape, and related transforms Mathematics and Physics, Lectures on recent results, 1984.

J. Antoine, P. Carrette, R. Murenzi, and B. Piette, Image analysis with two-dimensional continuous wavelet transform. Signal Process, pp.241-272, 1993.

I. Daubechies, Ten Lectures on Wavelets, CBMS-NSF, SIAM Lecture Series, 1992.

S. G. 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

M. Vetterli and J. Kova?evi´kova?evi´c, Wavelets and Subband Coding, 1995.

A. Cohen, R. De-vore, P. Petrushev, and H. Xu, Non linear approximation and the space BV (R 2 ), Am. J. Math, vol.121, pp.587-628, 1999.

A. Cohen, I. Daubechies, and J. Feauveau, Biorthogonal bases of compactly supported wavelets, Communications on Pure and Applied Mathematics, vol.10, issue.5, pp.485-560, 1992.
DOI : 10.1002/cpa.3160450502

O. Rioul and P. Duhamel, Fast algorithms for discrete and continuous wavelet transforms, IEEE Transactions on Information Theory, vol.38, issue.2, pp.569-586, 1992.
DOI : 10.1109/18.119724

M. J. Smith and W. C. Chung, Recursive time-varying filter banks for subband image coding, IEEE Transactions on Image Processing, vol.4, issue.7, pp.885-895, 1995.
DOI : 10.1109/83.392331

T. Cai, inequality approach, The Annals of Statistics, vol.27, issue.3, pp.898-924, 1999.
DOI : 10.1214/aos/1018031262

P. Müller and B. Vidakovic, Bayesian Inference in Wavelet Based Models, volume 141 of Lecture Notes in Computer Science, 1999.

J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, Image denoising using scale mixtures of gaussians in the wavelet domain, IEEE Transactions on Image Processing, vol.12, issue.11, pp.1338-1351, 2003.
DOI : 10.1109/TIP.2003.818640

C. Chaux, L. Duval, A. Benazza-benyahia, and J. Pesquet, A Nonlinear Stein-Based Estimator for Multichannel Image Denoising, IEEE Transactions on Signal Processing, vol.56, issue.8, pp.3855-3870, 2008.
DOI : 10.1109/TSP.2008.921757

URL : https://hal.archives-ouvertes.fr/hal-00617318

R. Coifman and D. Donoho, Translation-Invariant De-Noising, Wavelets and Statistics, pp.125-150, 1995.
DOI : 10.1007/978-1-4612-2544-7_9

M. J. Shensa, The discrete wavelet transform: wedding the a trous and Mallat algorithms, IEEE Transactions on Signal Processing, vol.40, issue.10, pp.2464-2482, 1992.
DOI : 10.1109/78.157290

A. Chambolle and B. J. Lucier, Interpreting translation-invariant wavelet shrinkage as a new image smoothing scale space, IEEE Transactions on Image Processing, vol.10, issue.7, pp.993-1000, 2001.
DOI : 10.1109/83.931093

P. P. Vaidyanathan, Multirate systems and filter banks, 1993.

T. Blu and M. Unser, The fractional spline wavelet transform: definition end implementation, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100), pp.512-515, 2000.
DOI : 10.1109/ICASSP.2000.862030

X. Zhang, M. D. Desai, and Y. Peng, Orthogonal complex filter banks and wavelets: some properties and design, IEEE Transactions on Signal Processing, vol.47, issue.4, pp.1039-1048, 1999.
DOI : 10.1109/78.752601

P. Steffen, P. N. Heller, R. A. Gopinath, and C. S. Burrus, Theory of regular M-band wavelet bases, IEEE Transactions on Signal Processing, vol.41, issue.12, pp.413497-3511, 1993.
DOI : 10.1109/78.258088

P. Auscher, Wavelet bases for L 2 (R) with rational dilation factor, Wavelets and their applications, pp.439-452, 1992.

T. Blu, Iterated filter banks with rational rate changes connection with discrete wavelet transforms, IEEE Transactions on Signal Processing, vol.41, issue.12, pp.3232-3244, 1993.
DOI : 10.1109/78.258070

T. Blu, A new design algorithm for two-band orthonormal rational filter banks and orthonormal rational wavelets, IEEE Transactions on Signal Processing, vol.46, issue.6, pp.1494-1504, 1998.
DOI : 10.1109/78.678463

A. Baussard, F. Nicolier, and F. Truchetet, Rational multiresolution analysis and fast wavelet transform: application to wavelet shrinkage denoising. Signal Process [78] ? I. Bayram and I. W. Selesnick. Frequency-domain design of overcomplete rational-dilation wavelet transforms, IEEE Trans. Signal Process, vol.84, issue.578, pp.1735-17472957, 2004.

Z. Xiong, O. G. Guleryuz, and M. T. Orchard, A DCT-based embedded image coder, IEEE Signal Processing Letters, vol.3, issue.11, pp.289-290, 1996.
DOI : 10.1109/97.542157

H. S. Malvar, Fast progressive image coding without wavelets, Proceedings DCC 2000. Data Compression Conference, pp.243-252, 2000.
DOI : 10.1109/DCC.2000.838164

H. S. Malvar, A. Hallapuro, M. Karczewicz, and L. Kerofsky, Low-complexity transform and quantization in H.264/AVC, IEEE Transactions on Circuits and Systems for Video Technology, vol.13, issue.7, pp.598-603, 2003.
DOI : 10.1109/TCSVT.2003.814964

C. P. Rosiene and T. Q. Nguyen, Tensor-product wavelet vs. Mallat decomposition: a comparative analysis, ISCAS'99. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems VLSI (Cat. No.99CH36349), pp.431-434, 1999.
DOI : 10.1109/ISCAS.1999.778877

D. Xu and M. N. Do, Anisotropic 2D wavelet packets and rectangular tiling: theory and algorithms, Wavelets: Applications in Signal and Image Processing X, pp.619-630, 2003.
DOI : 10.1117/12.506601

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.212.7474

G. P. Nason and B. W. Silverman, The Stationary Wavelet Transform and some Statistical Applications, Wavelets and Statistics, pp.281-300, 1995.
DOI : 10.1007/978-1-4612-2544-7_17

J. Pesquet, H. Krim, and H. Carfantan, Time-invariant orthonormal wavelet representations, IEEE Transactions on Signal Processing, vol.44, issue.8, pp.1964-1970, 1996.
DOI : 10.1109/78.533717

I. Cohen, S. Raz, and D. Malah, Orthonormal shift-invariant adaptive local trigonometric decomposition, Signal Processing, vol.57, issue.1, pp.43-64, 1997.
DOI : 10.1016/S0165-1684(96)00185-5

C. K. Chui, W. He, and J. Stöckler, Compactly supported tight and sibling frames with maximum vanishing moments, Applied and Computational Harmonic Analysis, vol.13, issue.3, pp.224-262, 2002.
DOI : 10.1016/S1063-5203(02)00510-9

I. Daubechies, B. Han, A. Ron, and Z. Shen, Framelets: MRA-based constructions of wavelet frames, Applied and Computational Harmonic Analysis, vol.14, issue.1, pp.1-46, 2003.
DOI : 10.1016/S1063-5203(02)00511-0

T. Aach and D. Kunz, A lapped directional transform for spectral image analysis and its application to restoration and enhancement, Signal Processing, vol.80, issue.11, pp.2347-2364, 2000.
DOI : 10.1016/S0165-1684(00)00122-5

T. Tanaka and Y. Yamashita, The Generalized Lapped Pseudo-Biorthogonal Transform: Oversampled Linear-Phase Perfect Reconstruction Filterbanks With Lattice Structures, IEEE Transactions on Signal Processing, vol.52, issue.2, pp.434-446, 2004.
DOI : 10.1109/TSP.2003.821102

J. Zhou and M. N. Do, Multidimensional oversampled filter banks, Wavelets XI, pp.591424-591425, 2005.
DOI : 10.1117/12.618209

T. Tanaka, A Direct Design of Oversampled Perfect Reconstruction FIR Filter Banks, IEEE Transactions on Signal Processing, vol.54, issue.8, pp.3011-3022, 2006.
DOI : 10.1109/TSP.2006.875384

J. Gauthier, L. Duval, and J. Pesquet, Optimization of Synthesis Oversampled Complex Filter Banks, IEEE Transactions on Signal Processing, vol.57, issue.10, pp.3827-3843, 2009.
DOI : 10.1109/TSP.2009.2023947

URL : https://hal.archives-ouvertes.fr/hal-00405293

E. P. Simoncelli, W. T. Freeman, E. H. Adelson, and D. J. Heeger, Shiftable multiscale transforms, IEEE Transactions on Information Theory, vol.38, issue.2, pp.587-607, 1992.
DOI : 10.1109/18.119725

E. P. Simoncelli and W. T. Freeman, The steerable pyramid: a flexible architecture for multi-scale derivative computation, Proceedings., International Conference on Image Processing, pp.444-447, 1995.
DOI : 10.1109/ICIP.1995.537667

M. Unser and D. Van-de-ville, The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression, IEEE Transactions on Image Processing, vol.17, issue.11, pp.2040-2052, 2008.
DOI : 10.1109/TIP.2008.2004607

D. Van-de-ville and M. Unser, Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid, IEEE Transactions on Image Processing, vol.17, issue.11, pp.2063-2080, 2008.
DOI : 10.1109/TIP.2008.2004797

B. Forster, T. Blu, D. Van-de-ville, and M. Unser, Shift-invariant spaces from rotation-covariant functions, Applied and Computational Harmonic Analysis, vol.25, issue.2, pp.240-265, 2008.
DOI : 10.1016/j.acha.2007.11.002

D. Marr, Vision: A Computational Investigation into the Human Representation and Processing of Visual Information, 1982.
DOI : 10.7551/mitpress/9780262514620.001.0001

M. Unser, N. Chenouard, and D. Van-de-ville, Steerable pyramids and tight wavelet frames in L 2 (R d ), IEEE Trans. Image Process, 2011.

D. Gabor, Theory of communication, Journal of the Institution of Electrical Engineers - Part I: General, vol.94, issue.73, pp.429-457, 1946.
DOI : 10.1049/ji-1.1947.0015

F. W. King, Hilbert Transforms, volume 125 of Encyclopedia Of Mathematics And Its Applications, 2009.

S. L. Hahn, Multidimensional complex signals with single-orthant spectra, Proc. IEEE, pp.1287-1300, 1992.
DOI : 10.1109/5.158601

K. N. Chaudhury and M. Unser, On the Shiftability of Dual-Tree Complex Wavelet Transforms, IEEE Transactions on Signal Processing, vol.58, issue.1, pp.221-232, 2010.
DOI : 10.1109/TSP.2009.2028962

J. Antoine, R. Murenzi, and P. Vandergheynst, Directional Wavelets Revisited: Cauchy Wavelets and Symmetry Detection in Patterns, Applied and Computational Harmonic Analysis, vol.6, issue.3, pp.314-345, 1999.
DOI : 10.1006/acha.1998.0255

P. Abry and P. Flandrin, Multiresolution transient detection, Proceedings of IEEE-SP International Symposium on Time- Frequency and Time-Scale Analysis, pp.225-228, 1994.
DOI : 10.1109/TFSA.1994.467252

G. Beylkin and B. Torrésani, Transformation de Hilbert et bancs de filtres In Colloque temps-fréquence, ondelettes et multirésolution : théorie, modèles et applications, pp.1-4, 1994.

J. Weiss, The Hilbert transform of wavelets are wavelets, Applied Mathematics Group, 1995.

G. Beylkin and B. Torrésani, Implementation of Operators via Filter Banks, Applied and Computational Harmonic Analysis, vol.3, issue.2, pp.164-185, 1996.
DOI : 10.1006/acha.1996.0014

URL : https://hal.archives-ouvertes.fr/hal-01223132

N. G. Kingsbury, The dual-tree complex wavelet transform: a new technique for shift invariance and directional filters, Proc. IEEE Digital Signal Process. Workshop, 1998.

N. G. Kingsbury, Image processing with complex wavelets, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.357, issue.1760, pp.2543-2560, 1999.
DOI : 10.1098/rsta.1999.0447

I. W. Selesnick, Hilbert transform pairs of wavelet bases. Signal Process, Lett, vol.8, issue.6, pp.170-173, 2001.

I. W. Selesnick, R. G. Baraniuk, and N. G. Kingsbury, The dual-tree complex wavelet transform, IEEE Signal Processing Magazine, vol.22, issue.6, pp.123-151, 2005.
DOI : 10.1109/MSP.2005.1550194

C. Chaux, L. Duval, and J. Pesquet, Image analysis using a dual-tree M-band wavelet transform, IEEE Transactions on Image Processing, vol.15, issue.8, pp.2397-2412, 2006.
DOI : 10.1109/TIP.2006.875178

URL : https://hal.archives-ouvertes.fr/hal-00621948

A. Jalobeanu, N. Kingsbury, and J. Zerubia, Image deconvolution using hidden Markov tree modeling of complex wavelet packets [116] ? I. Bayram and I. W. Selesnick. On the dual-tree complex wavelet packet and M -band transforms, Proc. Int. Conf. Image Process, pp.201-2042298, 2001.

R. A. Gopinath, The phaselet transform-an integral redundancy nearly shift-invariant wavelet transform, IEEE Transactions on Signal Processing, vol.51, issue.7, pp.1792-1805, 2003.
DOI : 10.1109/TSP.2003.812833

R. A. Gopinath, Phaselets of framelets, IEEE Transactions on Signal Processing, vol.53, issue.5, pp.1794-1806, 2005.
DOI : 10.1109/TSP.2005.845471

I. W. Selesnick, The characterization and design of Hilbert transform pairs of wavelet bases, Proc. Conf. Inform. Sciences Syst, 2001.

K. N. Chaudhury and M. Unser, Gabor wavelet analysis and the fractional Hilbert transform, Wavelets XIII, pp.74460-74461, 2009.
DOI : 10.1117/12.824863.1

K. N. Chaudhury and M. Unser, Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms, IEEE Transactions on Signal Processing, vol.57, issue.9, pp.3411-3425, 2009.
DOI : 10.1109/TSP.2009.2020767

T. Bülow and G. Sommer, Hypercomplex signals-a novel extension of the analytic signal to the multidimensional case, IEEE Transactions on Signal Processing, vol.49, issue.11, pp.2844-2852, 2001.
DOI : 10.1109/78.960432

W. Chan, H. Choi, and R. G. Baraniuk, Directional hypercomplex wavelets for multidimensional signal analysis and processing, Proc. Int. Conf. Acoust. Speech Signal Process, pp.996-999, 2004.

J. Wedekind, B. P. Amavasai, and K. Dutton, Steerable Filters Generated with the Hypercomplex Dual-Tree Wavelet Transform, 2007 IEEE International Conference on Signal Processing and Communications, pp.1291-1294, 2007.
DOI : 10.1109/ICSPC.2007.4728563

M. Unser, D. Sage, and D. Van-de-ville, Multiresolution Monogenic Signal Analysis Using the Riesz–Laplace Wavelet Transform, IEEE Transactions on Image Processing, vol.18, issue.11, pp.2402-2418, 2009.
DOI : 10.1109/TIP.2009.2027628

M. Unser and D. Van-de-ville, Higher-order Riesz transforms and steerable wavelet frames, Proc. Int. Conf. Image Process, pp.3757-3760, 2009.

M. Felsberg, Low-level image processing with the structure multivector, 2002.

S. C. Olhede and G. Metikas, The Monogenic Wavelet Transform, IEEE Transactions on Signal Processing, vol.57, issue.9, pp.3426-3441, 2009.
DOI : 10.1109/TSP.2009.2023397

S. Held, M. Storath, P. Massopust, and B. Forster, Steerable Wavelet Frames Based on the Riesz Transform, IEEE Transactions on Image Processing, vol.19, issue.3, pp.653-667, 2010.
DOI : 10.1109/TIP.2009.2036713

R. Van-spaendonck, F. Fernandes, M. Coates, and C. Burrus, Non-redundant, directionally selective, complex wavelets, Proceedings 2000 International Conference on Image Processing (Cat. No.00CH37101), pp.379-382, 2000.
DOI : 10.1109/ICIP.2000.899399

F. C. Fernandes, R. L. Van-spaendonck, and C. S. Burrus, A directional, shift insensitive, low-redundancy, wavelet transform, Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205), pp.618-621, 2001.
DOI : 10.1109/ICIP.2001.959121

F. C. Fernandes, R. L. Van-spaendonck, and C. S. Burrus, A new framework for complex wavelet transforms, IEEE Transactions on Signal Processing, vol.51, issue.7, pp.1825-1837, 2003.
DOI : 10.1109/TSP.2003.812841

F. C. Fernandes, M. Wakin, and R. Baraniuk, Non-redundant, linear-phase, semiorthogonal , directional complex wavelets, Proc. Int. Conf. Acoust. Speech Signal Process, 2004.

F. C. Fernandes, R. L. Van-spaendonck, and C. S. Burrus, Multidimensional, mapping-based complex wavelet transforms, IEEE Transactions on Image Processing, vol.14, issue.1, pp.110-124, 2005.
DOI : 10.1109/TIP.2004.838701

L. Gagnon, J. Lina, and B. Goulard, Sharpening enhancement of digitized mammograms with complex symmetric Daubechies wavelets, Proceedings of 17th International Conference of the Engineering in Medicine and Biology Society, 1995.
DOI : 10.1109/IEMBS.1995.575241

B. Belzer, J. Lina, and J. Villasenor, Complex, linear-phase filters for efficient image coding, IEEE Transactions on Signal Processing, vol.43, issue.10, pp.2425-2427, 1995.
DOI : 10.1109/78.469843

D. Clonda, J. Lina, and B. Goulard, Complex Daubechies wavelets: properties and statistical image modelling, Signal Processing, vol.84, issue.1, pp.1-23, 2004.
DOI : 10.1016/j.sigpro.2003.06.001

Z. Wang and E. P. Simoncelli, Translation insensitive image similarity in complex wavelet domain, Proc. Int. Conf. Acoust. Speech Signal Process, pp.573-576, 2005.

M. P. Sampat, Z. Wang, S. Gupta, A. C. Bovik, and M. K. Markey, Complex Wavelet Structural Similarity: A New Image Similarity Index, IEEE Transactions on Image Processing, vol.18, issue.11, pp.2402-2418, 2009.
DOI : 10.1109/TIP.2009.2025923

L. Shen, M. Papadakis, I. A. Kakadiaris, I. Konstantinidis, D. Kouri et al., Image Denoising Using a Tight Frame, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005., pp.1254-1263, 2006.
DOI : 10.1109/ICASSP.2005.1415486

R. H. Bamberger and M. J. Smith, A filter bank for the directional decomposition of images: theory and design, IEEE Transactions on Signal Processing, vol.40, issue.4, pp.882-893, 1992.
DOI : 10.1109/78.127960

M. J. Smith and T. P. Barnwell, A procedure for designing exact reconstruction filter banks for tree structured subband coders, Proc. Int. Conf. Acoust. Speech Signal Process, pp.421-424, 1984.

X. G. Xia and B. W. Suter, A Family of Two-Dimensional Nonseparable Malvar Wavelets, Applied and Computational Harmonic Analysis, vol.2, issue.3, pp.243-256, 1995.
DOI : 10.1006/acha.1995.1017

S. Coulombe and E. Dubois, Multidimensional windows over arbitrary lattices and their application to FIR filter design, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings, pp.2383-2386, 1996.
DOI : 10.1109/ICASSP.1996.547762

J. Kova?evi´kova?evi´c and M. Vetterli, Nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for R/sup n/, IEEE Transactions on Information Theory, vol.38, issue.2, pp.533-555, 1992.
DOI : 10.1109/18.119722

J. Kova?evi´kova?evi´c and M. Vetterli, Nonseparable two- and three-dimensional wavelets, IEEE Transactions on Signal Processing, vol.43, issue.5, pp.1269-1273, 1995.
DOI : 10.1109/78.382414

J. Antoine, R. Murenzi, P. Vandergheynst, and S. Ali, Two-dimensional wavelets and their relatives, 2004.
DOI : 10.1017/CBO9780511543395

J. C. Feauveau, Analyse multirésolution pour les images avec un facteur de résolution ? 2

J. Faugère, F. Moreau-de-saint-martin, and F. Rouillier, Design of regular nonseparable bidimensional wavelets using Grobner basis techniques, IEEE Transactions on Signal Processing, vol.46, issue.4, pp.845-856, 1998.
DOI : 10.1109/78.668541

A. Ayache, Some Methods for Constructing Nonseparable, Orthonormal, Compactly Supported Wavelet Bases, Applied and Computational Harmonic Analysis, vol.10, issue.1, pp.99-111, 2001.
DOI : 10.1006/acha.2000.0325

S. Durand, M-band filtering and nonredundant directional wavelets, Applied and Computational Harmonic Analysis, vol.22, issue.1, pp.124-139, 2007.
DOI : 10.1016/j.acha.2006.05.006

URL : https://hal.archives-ouvertes.fr/hal-00204978

T. T. Nguyen and S. Oraintara, A Class of Multiresolution Directional Filter Banks, IEEE Transactions on Signal Processing, vol.55, issue.3, pp.949-961, 2007.
DOI : 10.1109/TSP.2006.887140

M. N. Do and M. Vetterli, The contourlet transform: an efficient directional multiresolution image representation, IEEE Transactions on Image Processing, vol.14, issue.12, pp.2091-2106, 2005.
DOI : 10.1109/TIP.2005.859376

A. L. Cunha, J. Zhou, and M. N. Do, The Nonsubsampled Contourlet Transform: Theory, Design, and Applications, IEEE Transactions on Image Processing, vol.15, issue.10, pp.3089-3101, 2006.
DOI : 10.1109/TIP.2006.877507

Y. M. Lu and M. N. Do, Multidimensional Directional Filter Banks and Surfacelets, IEEE Transactions on Image Processing, vol.16, issue.4, pp.918-931, 2007.
DOI : 10.1109/TIP.2007.891785

A. Averbuch, R. R. Coifman, D. L. Donoho, M. Elad, and M. Israeli, Fast and accurate Polar Fourier transform, Applied and Computational Harmonic Analysis, vol.21, issue.2, pp.145-167, 2006.
DOI : 10.1016/j.acha.2005.11.003

H. Knutsson and M. Andersson, Implications of invariance and uncertainty for local structure analysis filter sets. Signal Process, Image Comm, vol.20, pp.569-581, 2005.

D. Taubman and A. Zakhor, Orientation adaptive subband coding of images, IEEE Transactions on Image Processing, vol.3, issue.4, pp.421-437, 1994.
DOI : 10.1109/83.298396

J. E. Bresenham, Algorithm for computer control of a digital plotter, IBM Systems Journal, vol.4, issue.1, pp.25-30, 1965.
DOI : 10.1147/sj.41.0025

A. Rosenfeld and R. Klette, Digital straightness. Electron. Notes Theor, Comput. Sci, vol.46, pp.1-32, 2001.

X. Daragon, M. Couprie, and G. Bertrand, Discrete Frontiers, Discrete geometry for computer imagery, pp.236-245, 2003.
DOI : 10.1007/978-3-540-39966-7_22

URL : https://hal.archives-ouvertes.fr/hal-00622040

E. Andres and P. Carré, Ridgelet transform based onReveilì es discrete lines, Proc. IAPR Int. Conf. Discrete Geom. Comput. Imagery (DGCI), volume 2301 of Lecture Notes in Computer Science, pp.417-427, 2002.

V. Velisavljevi´cvelisavljevi´c, B. Beferull-lozano, M. Vetterli, and P. L. Dragotti, Directionlets: anisotropic multidirectional representation with separable filtering, IEEE Transactions on Image Processing, vol.15, issue.7, pp.1916-1933, 2006.
DOI : 10.1109/TIP.2006.877076

V. Chappelier and C. Guillemot, Oriented Wavelet Transform for Image Compression and Denoising, IEEE Transactions on Image Processing, vol.15, issue.10, pp.2892-2903, 2006.
DOI : 10.1109/TIP.2006.877526

URL : https://hal.archives-ouvertes.fr/inria-00504227

C. Chang and B. Girod, Direction-Adaptive Discrete Wavelet Transform for Image Compression, IEEE Transactions on Image Processing, vol.16, issue.5, pp.1289-1302, 2007.
DOI : 10.1109/TIP.2007.894242

Y. Tanaka, M. Ikehara, and T. Q. Nguyen, Multiresolution Image Representation Using Combined 2-D and 1-D Directional Filter Banks, IEEE Transactions on Image Processing, vol.18, issue.2, pp.269-280, 2009.
DOI : 10.1109/TIP.2008.2008078

Y. Tanaka, M. Hasegawa, S. Kato, M. Ikehara, and T. Q. Nguyen, Adaptive Directional Wavelet Transform Based on Directional Prefiltering, IEEE Transactions on Image Processing, vol.19, issue.4, pp.934-945, 2010.
DOI : 10.1109/TIP.2009.2038820

Z. Zhang, S. Ma, H. Liu, and Y. Gong, An edge detection approach based on directional wavelet transform, Computers & Mathematics with Applications, vol.57, issue.8, pp.1265-1271, 2009.
DOI : 10.1016/j.camwa.2008.11.013

J. Krommweh and G. Plonka, Directional Haar wavelet frames on triangles, Applied and Computational Harmonic Analysis, vol.27, issue.2, pp.215-234, 2009.
DOI : 10.1016/j.acha.2009.03.002

URL : http://doi.org/10.1016/j.acha.2009.03.002

M. Said, J. Lachaud, and F. Feschet, Multiscale Discrete Geometry, Proc. IAPR Int. Conf. Discrete Geom. Comput. Imagery (DGCI), Lecture Notes in Computer Science, pp.118-131, 2009.
DOI : 10.1007/11919629_22

URL : https://hal.archives-ouvertes.fr/hal-00413681

W. T. Freeman and E. H. Adelson, Steerable filters for early vision, image analysis, and wavelet decomposition, [1990] Proceedings Third International Conference on Computer Vision, pp.406-415, 1990.
DOI : 10.1109/ICCV.1990.139562

W. T. Freeman and E. H. Adelson, The design and use of steerable filters, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.13, issue.9, pp.891-906, 1991.
DOI : 10.1109/34.93808

W. T. Freeman, Steerable Filters and Local Analysis of Image Structure, 1992.

E. P. Simoncelli and H. Farid, Steerable wedge filters for local orientation analysis, IEEE Transactions on Image Processing, vol.5, issue.9, pp.1377-1382, 1996.
DOI : 10.1109/83.535851

A. A. Bharath and J. Ng, A steerable complex wavelet construction and its application to image denoising, IEEE Transactions on Image Processing, vol.14, issue.7, pp.948-959, 2005.
DOI : 10.1109/TIP.2005.849295

X. Shi, A. L. Castro, R. Manduchi, and R. Montgomery, Rotational invariant operators based on steerable filter banks. Signal Process, Lett, vol.13, issue.11, 2006.

T. S. Lee, Image representation using 2D Gabor wavelets, IEEE Trans. Patt. Anal. Mach. Int, vol.18, issue.10, pp.959-971, 1996.

O. Nestares, R. Navarro, J. Portilla, and A. Tabernero, Efficient spatial-domain implementation of a multiscale image representation based on Gabor functions, Journal of Electronic Imaging, vol.7, issue.1, pp.166-173, 1998.
DOI : 10.1117/1.482638

P. Vandergheynst and J. Gobbers, Directional dyadic wavelet transforms: design and algorithms, IEEE Transactions on Image Processing, vol.11, issue.4, pp.363-372, 2002.
DOI : 10.1109/TIP.2002.999670

L. Jacques and J. Antoine, MULTISELECTIVE PYRAMIDAL DECOMPOSITION OF IMAGES: WAVELETS WITH ADAPTIVE ANGULAR SELECTIVITY, International Journal of Wavelets, Multiresolution and Information Processing, vol.05, issue.05, pp.785-814, 2007.
DOI : 10.1142/S0219691307002051

E. J. Candès and D. L. Donoho, Ridgelets: a key to higher-dimensional intermittency?, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.357, issue.1760, pp.2495-2509, 1999.
DOI : 10.1098/rsta.1999.0444

D. L. Donoho, Tight frames of k-plane ridgelets and the problem of representing objects that are smooth away from d-dimensional singularities in Rn, Proc. Nat. Acad. Sci. U.S.A, pp.1828-1833, 1999.
DOI : 10.1073/pnas.96.5.1828

R. A. Zuidwijk, Directional and Time-Scale Wavelet Analysis, SIAM Journal on Mathematical Analysis, vol.31, issue.2, pp.416-430, 2000.
DOI : 10.1137/S0036141098333359

S. R. Deans, The Radon transform and some of its applications, 1983.

M. N. Do and M. Vetterli, The finite ridgelet transform for image representation, IEEE Transactions on Image Processing, vol.12, issue.1, pp.16-28, 2003.
DOI : 10.1109/TIP.2002.806252

J. Starck, E. J. Candès, and D. L. Donoho, The curvelet transform for image denoising, IEEE Transactions on Image Processing, vol.11, issue.6, pp.670-685, 2002.
DOI : 10.1109/TIP.2002.1014998

D. Helbert and P. , 3-D Discrete Analytical Ridgelet Transform, IEEE Transactions on Image Processing, vol.15, issue.12, pp.3701-3714, 2006.
DOI : 10.1109/TIP.2006.881936

URL : https://hal.archives-ouvertes.fr/hal-00331384

D. L. Donoho and A. G. Flesia, Digital Ridgelet Transform Based on True Ridge Functions, Studies in Computational Mathematics, vol.10, pp.1-30, 2003.
DOI : 10.1016/S1570-579X(03)80029-0

E. J. Candès and D. L. Donoho, singularities, Communications on Pure and Applied Mathematics, vol.9, issue.7, pp.219-266, 2003.
DOI : 10.1002/cpa.10116

A. B. Watson, The cortex transform: Rapid computation of simulated neural images, Computer Vision, Graphics, and Image Processing, vol.39, issue.3, pp.311-327, 1987.
DOI : 10.1016/S0734-189X(87)80184-6

E. J. Candès and D. L. Donoho, Continuous curvelet transform, Applied and Computational Harmonic Analysis, vol.19, issue.2, pp.162-197, 2003.
DOI : 10.1016/j.acha.2005.02.003

E. J. Candès and D. L. Donoho, Continuous curvelet transform, Applied and Computational Harmonic Analysis, vol.19, issue.2, pp.198-222, 2003.
DOI : 10.1016/j.acha.2005.02.004

E. J. Candès, L. Demanet, D. L. Donoho, and L. Ying, Fast Discrete Curvelet Transforms, Multiscale Modeling & Simulation, vol.5, issue.3, pp.861-899, 2006.
DOI : 10.1137/05064182X

E. J. Candès and D. L. Donoho, singularities, Communications on Pure and Applied Mathematics, vol.9, issue.7, pp.219-266, 2004.
DOI : 10.1002/cpa.10116

M. Storath, Directional Multiscale Amplitude and Phase Decomposition by the Monogenic Curvelet Transform, SIAM Journal on Imaging Sciences, vol.4, issue.1, pp.57-78, 2011.
DOI : 10.1137/100803924

K. Guo and D. Labate, Optimally Sparse Multidimensional Representation Using Shearlets, SIAM Journal on Mathematical Analysis, vol.39, issue.1, pp.298-318, 2007.
DOI : 10.1137/060649781

P. Kittipoom, G. Kutyniok, and W. Lim, Irregular Shearlet Frames: Geometry and??Approximation Properties, Journal of Fourier Analysis and Applications, vol.132, issue.4, pp.1-36, 2010.
DOI : 10.1007/s00041-010-9163-0

URL : http://arxiv.org/abs/1002.2657

G. Kutyniok and D. Labate, The construction of regular and irregular shearlet frames, J. Wavelet Theory Appl, vol.1, pp.1-10, 2007.

W. Lim, The discrete shearlet transform: A new directional transform and compactly supported shearlet frames, IEEE Trans. Image Process, vol.19, issue.5, pp.1166-1180, 2010.

J. Xu, L. Yang, and D. Wu, Ripplet: A new transform for image processing, Journal of Visual Communication and Image Representation, vol.21, issue.7, pp.627-639, 2010.
DOI : 10.1016/j.jvcir.2010.04.002

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.7043

Y. Lu and M. N. Do, CRISP contourlets: a critically sampled directional multiresolution image representation, Wavelets: Applications in Signal and Image Processing X, pp.655-665, 2003.
DOI : 10.1117/12.506566

F. G. Meyer and R. R. Coifman, Brushlets: A Tool for Directional Image Analysis and Image Compression, Applied and Computational Harmonic Analysis, vol.4, issue.2, pp.147-187, 1997.
DOI : 10.1006/acha.1997.0208

L. Demanet and L. Ying, Wave atoms and sparsity of oscillatory patterns, Applied and Computational Harmonic Analysis, vol.23, issue.3, pp.368-387, 2007.
DOI : 10.1016/j.acha.2007.03.003

B. K. Natarajan, Sparse Approximate Solutions to Linear Systems, SIAM Journal on Computing, vol.24, issue.2, pp.227-234, 1995.
DOI : 10.1137/S0097539792240406

S. Mallat and Z. Zhang, Matching pursuits with time-frequency dictionaries, IEEE Transactions on Signal Processing, vol.41, issue.12, pp.3397-3415, 1993.
DOI : 10.1109/78.258082

Y. C. Pati, R. Rezaifar, and P. S. Krishnaprasa, Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers, 1993.
DOI : 10.1109/ACSSC.1993.342465

J. A. Tropp, Greed is Good: Algorithmic Results for Sparse Approximation, IEEE Transactions on Information Theory, vol.50, issue.10, pp.2231-2242, 2004.
DOI : 10.1109/TIT.2004.834793

D. L. Donoho, M. Elad, and V. N. Temlyakov, Stable recovery of sparse overcomplete representations in the presence of noise, IEEE Transactions on Information Theory, vol.52, issue.1, pp.6-18, 2006.
DOI : 10.1109/TIT.2005.860430

S. S. Chen, D. L. Donoho, and M. A. Saunders, Atomic Decomposition by Basis Pursuit, SIAM Journal on Scientific Computing, vol.20, issue.1, pp.33-61, 1998.
DOI : 10.1137/S1064827596304010

I. Daubechies, R. Devore, M. Fornasier, and S. Güntürk, Iteratively reweighted least squares minimization for sparse recovery, Communications on Pure and Applied Mathematics, vol.58, issue.1, pp.1-38, 2010.
DOI : 10.1002/cpa.20303

P. L. Combettes and V. R. Wajs, Signal Recovery by Proximal Forward-Backward Splitting, Multiscale Modeling & Simulation, vol.4, issue.4, pp.1168-1200, 2005.
DOI : 10.1137/050626090

URL : https://hal.archives-ouvertes.fr/hal-00017649

P. L. Combettes and J. Pesquet, Proximal splitting methods in signal processing Fixed-point algorithms for inverse problems in science and engineering, 2010.

J. A. Tropp, Just relax: convex programming methods for identifying sparse signals in noise, IEEE Transactions on Information Theory, vol.52, issue.3, pp.1030-1051, 2006.
DOI : 10.1109/TIT.2005.864420

P. Vandergheynst and P. Frossard, Image coding using redundant dictionaries, Document and image compression, 2006.

]. G. Monaci, P. Escoda, and . Vandergheynst, Analysis of multimodal sequences using geometric video representations, Signal Processing, vol.86, issue.12, pp.3534-3548, 2006.
DOI : 10.1016/j.sigpro.2006.02.044

R. Sala-llonch, E. Kokiopoulou, I. To?i´to?i´c, and P. Frossard, 3D face recognition with sparse spherical representations, Pattern Recognition, vol.43, issue.3, pp.824-834, 2010.
DOI : 10.1016/j.patcog.2009.07.005

L. Jacques and C. D. Vleeschouwer, A Geometrical Study of Matching Pursuit Parametrization, IEEE Transactions on Signal Processing, vol.56, issue.7, pp.2835-2848, 2008.
DOI : 10.1109/TSP.2008.917379

F. Bergeaud and S. Mallat, Matching pursuit: Adaptive representations of images and sounds, Comput. Appl. Math, vol.15, issue.2, pp.97-109, 1996.

R. Figueras, P. Ventura, P. Vandergheynst, and . Frossard, Low-rate and flexible image coding with redundant representations, IEEE Transactions on Image Processing, vol.15, issue.3, pp.726-739, 2006.
DOI : 10.1109/TIP.2005.860596

R. Neff and A. Zakhor, Very low bit-rate video coding based on matching pursuits, IEEE Transactions on Circuits and Systems for Video Technology, vol.7, issue.1, pp.158-171, 1997.
DOI : 10.1109/76.554427

L. I. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena, vol.60, issue.1-4, pp.259-268, 1992.
DOI : 10.1016/0167-2789(92)90242-F

J. Starck, M. Elad, and D. L. Donoho, Redundant Multiscale Transforms and Their Application for Morphological Component Separation, Adv. Imag. Electron Phys, vol.132, pp.287-348, 2004.
DOI : 10.1016/S1076-5670(04)32006-9

R. R. Coifman and M. V. Wickerhauser, Entropy-based algorithms for best basis selection, IEEE Transactions on Information Theory, vol.38, issue.2, pp.713-718, 1992.
DOI : 10.1109/18.119732

L. Breiman, J. H. Friedman, R. A. Olshen, and C. J. Stone, Classification and Regression Trees, 1984.

D. L. Donoho, CART and best-ortho-basis: a connection, The Annals of Statistics, vol.25, issue.5, pp.1870-1911, 1997.
DOI : 10.1214/aos/1069362377

M. V. Wickerhauser, INRIA lectures on wavelet packet algorithms. Lecture notes, INRIA, 1991.

A. Cohen and N. Dyn, Nonstationary Subdivision Schemes, Multiresolution Analysis, and Wavelet Packets, Signal and image representation in combined spaces of Wavelet analysis and its applications, pp.189-200, 1998.
DOI : 10.1016/S1874-608X(98)80008-3

N. Ouarti and G. Peyré, Best basis search in a non-stationary wavelet packets dictionary, Proc. Int. Conf. Image Process, 2009.

D. L. Donoho, Wedgelets: nearly minimax estimation of edges, The Annals of Statistics, vol.27, issue.3, pp.859-897, 1999.
DOI : 10.1214/aos/1018031261

R. Shukla, P. L. Dragotti, M. N. Do, and M. Vetterli, Rate-distortion optimized tree-structured compression algorithms for piecewise polynomial images, IEEE Transactions on Image Processing, vol.14, issue.3, pp.343-359, 2005.
DOI : 10.1109/TIP.2004.840710

URL : http://infoscience.epfl.ch/record/33817

A. A. Kassim, W. S. Lee, and D. Zonoobi, Hierarchical Segmentation-Based Image Coding Using Hybrid Quad-Binary Trees, IEEE Transactions on Image Processing, vol.18, issue.6, pp.1284-291, 2009.
DOI : 10.1109/TIP.2009.2017339

F. Friedrich, L. Demaret, H. Fuhr, and K. Wicker, Efficient Moment Computation over Polygonal Domains with an Application to Rapid Wedgelet Approximation, SIAM Journal on Scientific Computing, vol.29, issue.2, pp.842-863, 2007.
DOI : 10.1137/050646597

R. M. Willett and R. D. Nowak, Platelets: a multiscale approach for recovering edges and surfaces in photon-limited medical imaging, IEEE Transactions on Medical Imaging, vol.22, issue.3, pp.332-350, 2003.
DOI : 10.1109/TMI.2003.809622

V. Chandrasekaran, M. B. Wakin, D. Baron, and R. G. Baraniuk, Representation and Compression of Multidimensional Piecewise Functions Using <emphasis emphasistype="italic">Surflets</emphasis>, IEEE Transactions on Information Theory, vol.55, issue.1, pp.374-400, 2009.
DOI : 10.1109/TIT.2008.2008153

L. Pennec and S. Mallat, Bandelet Image Approximation and Compression, Multiscale Modeling & Simulation, vol.4, issue.3, pp.992-1039, 2005.
DOI : 10.1137/040619454

M. Wakin, J. Romberg, H. Choi, and R. Baraniuk, Wavelet-domain approximation and compression of piecewise smooth images, IEEE Transactions on Image Processing, vol.15, issue.5, pp.1071-1087, 2006.
DOI : 10.1109/TIP.2005.864175

G. Peyré and S. Mallat, Orthogonal bandelet bases for geometric images approximation, Communications on Pure and Applied Mathematics, vol.15, issue.5, pp.1173-1212, 2008.
DOI : 10.1002/cpa.20242

G. Plonka, The Easy Path Wavelet Transform: A New Adaptive Wavelet Transform for Sparse Representation of Two-Dimensional Data, Multiscale Modeling & Simulation, vol.7, issue.3, pp.1474-1496, 2009.
DOI : 10.1137/080719248

E. J. Candès, Compressive sampling, Proc. Int. Congr. Mathematicians, pp.1433-1452, 2006.
DOI : 10.4171/022-3/69

G. Peyré, Best Basis Compressed Sensing, IEEE Transactions on Signal Processing, vol.58, issue.5, pp.2613-2622, 2010.
DOI : 10.1109/TSP.2010.2042490

S. Dekel and D. Leviatan, Adaptive Multivariate Approximation Using Binary Space Partitions and Geometric Wavelets, SIAM Journal on Numerical Analysis, vol.43, issue.2, pp.707-732, 2005.
DOI : 10.1137/040604649

L. Demaret, N. Dyn, and A. Iske, Image compression by linear splines over adaptive triangulations, Signal Processing, vol.86, issue.7, pp.1604-1616, 2006.
DOI : 10.1016/j.sigpro.2005.09.003

R. Distasi, M. Nappi, and S. Vitulano, Image compression by B-tree triangular coding, IEEE Transactions on Communications, vol.45, issue.9, pp.1095-1100, 1997.
DOI : 10.1109/26.623074

A. Cohen, N. Dyn, F. Hecht, and J. Mirebeau, Adaptive multiresolution analysis based on anisotropic triangulations, Mathematics of Computation, vol.81, issue.278, 2011.
DOI : 10.1090/S0025-5718-2011-02495-6

URL : https://hal.archives-ouvertes.fr/hal-00387804

M. Jansen, R. G. Baraniuk, and S. Lavu, Multiscale approximation of piecewise smooth two-dimensional functions using normal triangulated meshes, Applied and Computational Harmonic Analysis, vol.19, issue.1, pp.92-130, 2005.
DOI : 10.1016/j.acha.2005.02.006

W. Sweldens, The Lifting Scheme: A Construction of Second Generation Wavelets, SIAM Journal on Mathematical Analysis, vol.29, issue.2, pp.511-546, 1997.
DOI : 10.1137/S0036141095289051

N. Dyn, J. A. Gregory, and D. Levin, A 4-point interpolatory subdivision scheme for curve design, Computer Aided Geometric Design, vol.4, issue.4, pp.257-268, 1987.
DOI : 10.1016/0167-8396(87)90001-X

F. A. Bruekers and A. W. Van-den-enden, New networks for perfect inversion and perfect reconstruction, IEEE Journal on Selected Areas in Communications, vol.10, issue.1, pp.129-137, 1992.
DOI : 10.1109/49.124464

F. J. Hampson and J. Pesquet, M-band nonlinear subband decompositions with perfect reconstruction, IEEE Transactions on Image Processing, vol.7, issue.11, pp.1547-1560, 1998.
DOI : 10.1109/83.725362

I. Daubechies and W. Sweldens, Factoring wavelet transforms into lifting steps, J. Fourier Anal. Appl, vol.4, issue.3, pp.245-267, 1998.

D. Taubman, Adaptive, non-separable lifting transforms for image compression, Proceedings 1999 International Conference on Image Processing (Cat. 99CH36348), pp.772-776, 1999.
DOI : 10.1109/ICIP.1999.817221

O. Egger, W. Li, and M. Kunt, High compression image coding using an adaptive morphological subband decomposition, Proc. IEEE, pp.272-287, 1995.
DOI : 10.1109/5.364462

J. Goutsias and H. J. Heijmans, Nonlinear multiresolution signal decomposition schemes. I. Morphological pyramids, IEEE Transactions on Image Processing, vol.9, issue.11, pp.1862-1876, 2000.
DOI : 10.1109/83.877209

H. J. Heijmans and J. Goutsias, Nonlinear multiresolution signal decomposition schemes. II. Morphological wavelets, IEEE Transactions on Image Processing, vol.9, issue.11, pp.1897-1913, 2000.
DOI : 10.1109/83.877211

R. L. Claypoole, G. M. Davis, W. Sweldens, and R. G. Baraniuk, Nonlinear wavelet transforms for image coding via lifting, IEEE Transactions on Image Processing, vol.12, issue.12, pp.1449-1459, 2003.
DOI : 10.1109/TIP.2003.817237

A. Gouze, M. Antonini, M. Barlaud, and B. Macq, Design of Signal-Adapted Multidimensional Lifting Scheme for Lossy Coding, IEEE Transactions on Image Processing, vol.13, issue.12, pp.1589-1603, 2004.
DOI : 10.1109/TIP.2004.837556

M. Kâaniche, A. Benazza-benyahia, B. Pesquet-popescu, and J. Pesquet, Vector Lifting Schemes for Stereo Image Coding, IEEE Transactions on Image Processing, vol.18, issue.11, pp.2463-2475, 2009.
DOI : 10.1109/TIP.2009.2026672

G. Quellec, M. Lamard, G. Cazuguel, B. Cochener, and C. Roux, Adaptive Nonseparable Wavelet Transform via Lifting and its Application to Content-Based Image Retrieval, IEEE Transactions on Image Processing, vol.19, issue.1, pp.25-35, 2010.
DOI : 10.1109/TIP.2009.2030479

URL : https://hal.archives-ouvertes.fr/hal-00473899

M. Kâaniche, A. Benazza-benyahia, B. Pesquet-popescu, and J. Pesquet, Non separable lifting scheme with adaptive update step for still and stereo image coding. Signal Process, 2011.

A. Cohen and B. Matei, Nonlinear Subdivision Schemes: Applications to Image Processing, Tutorials on Multiresolution in Geometric Modelling Europ. summer school on principles of multiresolution in geometric modelling, pp.93-97, 2002.
DOI : 10.1007/978-3-662-04388-2_5

O. N. Gerek and A. E. Cetin, Adaptive polyphase subband decomposition structures for image compression, IEEE Transactions on Image Processing, vol.9, issue.10, pp.1649-1660, 2000.
DOI : 10.1109/83.869176

B. C. Yin, X. Li, Y. H. Shi, F. Z. Zhang, and N. Zhang, Directional lifting-based wavelet transform for multiple description image coding. Signal Process, Image Comm, vol.23, issue.1, pp.42-57, 2008.

H. J. Heijmans, B. Pesquet-popescu, and G. Piella, Building nonredundant adaptive wavelets by update lifting, Applied and Computational Harmonic Analysis, vol.18, issue.3, pp.252-281, 2005.
DOI : 10.1016/j.acha.2004.11.006

B. Pesquet-popescu and V. Bottreau, Three-dimensional lifting schemes for motion compensated video compression, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221), pp.1793-1796, 2001.
DOI : 10.1109/ICASSP.2001.941289

A. Secker and D. Taubman, Lifting-based invertible motion adaptive transform (LIMAT) framework for highly scalable video compression, IEEE Transactions on Image Processing, vol.12, issue.12, pp.1530-1542, 2003.
DOI : 10.1109/TIP.2003.819433

S. Mallat, Geometrical grouplets, Applied and Computational Harmonic Analysis, vol.26, issue.2, pp.161-180, 2009.
DOI : 10.1016/j.acha.2008.03.004

G. Peyré, Texture Synthesis with Grouplets, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.32, issue.4, pp.733-746, 2009.
DOI : 10.1109/TPAMI.2009.54

D. J. Heeger and J. R. Bergen, Pyramid-based texture analysis/synthesis, Proc. SIGGRAPH Int. Conf. Comput. Graph. Interactive Tech, pp.229-238, 1995.

J. Portilla and E. P. Simoncelli, A parametric texture model based on joint statistics of complex wavelet coefficients, International Journal of Computer Vision, vol.40, issue.1, pp.49-71, 2000.
DOI : 10.1023/A:1026553619983

A. A. Efros and W. T. Freeman, Image quilting for texture synthesis and transfer, Proceedings of the 28th annual conference on Computer graphics and interactive techniques , SIGGRAPH '01, pp.341-346, 2001.
DOI : 10.1145/383259.383296

D. M. Healy, D. N. Rockmore, P. J. Kostelec, and S. Moore, FFTs for the 2-Sphere-Improvements and Variations, Journal of Fourier Analysis and Applications, vol.9, issue.4, pp.341-385, 2003.
DOI : 10.1007/s00041-003-0018-9

J. R. Driscoll and D. M. Healy, Computing Fourier Transforms and Convolutions on the 2-Sphere, Advances in Applied Mathematics, vol.15, issue.2, pp.202-250, 1994.
DOI : 10.1006/aama.1994.1008

T. Bülow, Multiscale Image Processing on the Sphere, Proc. DAGM Symp. Patt. Recogn., Lecture Notes in Computer Science, pp.609-617, 2002.
DOI : 10.1007/3-540-45783-6_73

W. Freeden and U. Windheuser, Spherical wavelet transform and its discretization, Advances in Computational Mathematics, vol.31, issue.1, pp.51-94, 1996.
DOI : 10.1007/BF02124735

W. Freeden, T. Maier, and S. Zimmermann, A survey on wavelet methods for (geo)applications. Rev, Matemática Complutense, vol.16, issue.1, pp.277-310, 2003.

F. J. Narcowich, P. Petrushev, and J. D. Ward, Localized Tight Frames on Spheres, SIAM Journal on Mathematical Analysis, vol.38, issue.2, pp.574-594, 2006.
DOI : 10.1137/040614359

G. Kerkyacharian, P. Petrushev, D. Picard, and T. Willer, Needlet algorithms for estimation in inverse problems, Electronic Journal of Statistics, vol.1, issue.0, pp.30-76, 2007.
DOI : 10.1214/07-EJS014

F. Guilloux, G. Fa¨yfa¨y, and J. Cardoso, Practical wavelet design on the sphere, Applied and Computational Harmonic Analysis, vol.26, issue.2, pp.143-160, 2009.
DOI : 10.1016/j.acha.2008.03.003

URL : https://hal.archives-ouvertes.fr/hal-00155489

J. Antoine and P. Vandergheynst, Wavelets on the 2-Sphere: A Group-Theoretical Approach, Applied and Computational Harmonic Analysis, vol.7, issue.3, pp.262-291, 1999.
DOI : 10.1006/acha.1999.0272

J. Antoine, L. Demanet, L. Jacques, and P. Vandergheynst, Wavelets on the sphere: implementation and approximations, Applied and Computational Harmonic Analysis, vol.13, issue.3, pp.177-200, 2002.
DOI : 10.1016/S1063-5203(02)00507-9

Y. Wiaux, L. Jacques, and P. Vandergheynst, Correspondence Principle between Spherical and Euclidean Wavelets, The Astrophysical Journal, vol.632, issue.1, pp.15-28, 2005.
DOI : 10.1086/432926

I. Bogdanova, P. Vandergheynst, J. Antoine, L. Jacques, and M. Morvidone, Stereographic wavelet frames on the sphere, Applied and Computational Harmonic Analysis, vol.19, issue.2, pp.223-252, 2005.
DOI : 10.1016/j.acha.2005.05.001

L. Demanet and P. Vandergheynst, Gabor wavelets on the sphere, Wavelets: Applications in Signal and Image Processing X, pp.208-215, 2003.
DOI : 10.1117/12.506436

L. Cayón, J. L. Sanz, R. B. Barreiro, E. Martínez-gonzález, P. Vielva et al., Isotropic wavelets: a powerful tool to extract point sources from cosmic microwave background maps, Monthly Notices of the Royal Astronomical Society, vol.315, issue.4, pp.757-761, 2000.
DOI : 10.1046/j.1365-8711.2000.03462.x

P. Abrial, Y. Moudden, J. Starck, J. Bobin, B. Afeyan et al., Morphological Component Analysis and Inpainting on the Sphere: Application in Physics and Astrophysics, Journal of Fourier Analysis and Applications, vol.13, issue.6, pp.729-748, 2007.
DOI : 10.1007/s00041-006-6908-x

URL : https://hal.archives-ouvertes.fr/hal-00196082

Y. Wiaux, P. Vielva, R. B. Barreiro, E. Martínez-gonzález, and P. Vandergheynst, Non-Gaussianity analysis on local morphological measures of WMAP data, Monthly Notices of the Royal Astronomical Society, vol.385, issue.2, pp.939-947, 2008.
DOI : 10.1111/j.1365-2966.2008.12901.x

B. T. Yeo, W. Ou, and P. Golland, On the Construction of Invertible Filter Banks on the 2-Sphere, IEEE Transactions on Image Processing, vol.17, issue.3, pp.283-300, 2008.
DOI : 10.1109/TIP.2007.915550

P. Schröder and W. Sweldens, Spherical wavelets, Proceedings of the 22nd annual conference on Computer graphics and interactive techniques , SIGGRAPH '95, pp.161-172, 1995.
DOI : 10.1145/218380.218439

C. Lessig and F. E. Soho, Orthogonal and symmetric Haar wavelets on the sphere, ACM Trans. Graph, vol.274, issue.1, pp.1-4, 2008.

Y. Wiaux, L. Jacques, P. Vielva, and P. Vandergheynst, Fast Directional Correlation on the Sphere with Steerable Filters, The Astrophysical Journal, vol.652, issue.1, pp.820-832, 2006.
DOI : 10.1086/507692

P. Vandergheynst and Y. Wiaux, Wavelets on the sphere Four short courses in harmonic analysis: wavelets, frames, time-frequency methods, and applications to signal and image analysis, Birkhäuser, 2010.

Y. Wiaux, J. D. Mcewen, P. Vandergheynst, and O. Blanc, Exact reconstruction with directional wavelets on the sphere, Monthly Notices of the Royal Astronomical Society, vol.388, issue.2, pp.770-788, 2008.
DOI : 10.1111/j.1365-2966.2008.13448.x

J. Starck, Y. Moudden, P. Abrial, and M. Nguyen, Wavelets, ridgelets and curvelets on the sphere, Astronomy and Astrophysics, vol.446, issue.3, pp.1191-1204, 2006.
DOI : 10.1051/0004-6361:20053246

URL : https://hal.archives-ouvertes.fr/hal-00860058

D. Ro¸scaro¸sca, Wavelet Bases on the Sphere Obtained by Radial Projection, Journal of Fourier Analysis and Applications, vol.13, issue.4, pp.421-434, 2007.
DOI : 10.1007/s00041-006-6014-z

J. Antoine, D. Ro¸scaro¸sca, and P. Vandergheynst, Wavelet transform on manifolds: Old and new approaches, Special Issue on Continuous Wavelet Transform in Memory of Jean Morlet, pp.189-202, 2010.
DOI : 10.1016/j.acha.2009.10.002

J. Antoine, I. Bogdanova, and P. Vandergheynst, THE CONTINUOUS WAVELET TRANSFORM ON CONIC SECTIONS, International Journal of Wavelets, Multiresolution and Information Processing, vol.06, issue.02, pp.137-156, 2008.
DOI : 10.1142/S0219691308002288

W. Sweldens, The Lifting Scheme: A Custom-Design Construction of Biorthogonal Wavelets, Applied and Computational Harmonic Analysis, vol.3, issue.2, pp.186-200, 1996.
DOI : 10.1006/acha.1996.0015

M. Lounsbery, T. D. Derose, and J. Warren, Multiresolution analysis for surfaces of arbitrary topological type, ACM Transactions on Graphics, vol.16, issue.1, pp.34-73, 1997.
DOI : 10.1145/237748.237750

R. R. Coifman and M. Maggioni, Diffusion wavelets, Applied and Computational Harmonic Analysis, vol.21, issue.1, pp.53-94, 2006.
DOI : 10.1016/j.acha.2006.04.004

D. K. Hammond, P. Vandergheynst, and R. Gribonval, Wavelets on graphs via spectral graph theory, Applied and Computational Harmonic Analysis, vol.30, issue.2, pp.129-150, 2011.
DOI : 10.1016/j.acha.2010.04.005

URL : https://hal.archives-ouvertes.fr/inria-00541855