]. M. Bibliographie and . Albanesi, Thresholding wavelets for image compression, pp.374-389, 1997.

]. V. Algazi, G. E. Ford, and R. Potharlanka, Directional interpolation of images based on visual properties and rank order filtering, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing, pp.3005-3008, 1991.
DOI : 10.1109/ICASSP.1991.151035

]. E. Aly and H. Dubois, Regularized image up-sampling using a new observation model and the level set method, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429), pp.665-673, 2003.
DOI : 10.1109/ICIP.2003.1247332

]. E. Aly and H. A. Dubois, Image up-sampling using total-variation regularization with a new observation model, IEEE Transactions on Image Processing, vol.14, issue.10, pp.1647-1659, 2005.
DOI : 10.1109/TIP.2005.851684

]. C. Ballester, M. Bertalmio, V. Caselles, G. Sapiro, and J. Verdera, Filling-in by joint interpolation of vector fields and gray levels, IEEE Transactions on Image Processing, vol.10, issue.8, pp.1200-1211, 2001.
DOI : 10.1109/83.935036

]. S. Bayrakeri and R. M. Mersereau, A new method for directional image interpolation, 1995 International Conference on Acoustics, Speech, and Signal Processing, pp.2383-2386, 1995.
DOI : 10.1109/ICASSP.1995.479972

. Beylkin, Discrete radon transform, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.35, issue.2, pp.162-172, 1987.
DOI : 10.1109/TASSP.1987.1165108

]. A. Biancardi, L. Cinque, and L. Lombardi, Improvements to image magnification, Pattern Recognition, vol.35, issue.3, pp.677-687, 2002.
DOI : 10.1016/S0031-3203(01)00034-6

]. J. Bigun, J. M. Hans, and . Buf, Geometric image primitives by complex moments in Gabor space and the application to texture segmentation, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.648-650, 1992.
DOI : 10.1109/CVPR.1992.223118

I. Bt, 500-12. Methodology for the subjective assessment of the quality of television pictures, pp.500-512, 2009.

]. W. Burger, J. Mark, and . Burge, Principles of digital image processing : core algorithms, 2009.
DOI : 10.1007/978-1-84800-195-4

]. P. Burt and E. 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. Carrato, G. Ramponi, and S. Marsi, A simple edge-sensitive image interpolation filter, Proceedings of 3rd IEEE International Conference on Image Processing, pp.711-714, 1996.
DOI : 10.1109/ICIP.1996.560778

]. S. Chang, B. Yu, and M. Vetterli, Adaptive wavelet thresholding for image denoising and compression, IEEE Transactions on Image Processing, vol.9, issue.9, pp.1532-1546, 2000.
DOI : 10.1109/83.862633

]. Chang and B. Girod, Direction-Adaptive Discrete Wavelet Transform via Directional Lifting and Bandeletization, 2006 International Conference on Image Processing, pp.1149-1152, 2006.
DOI : 10.1109/ICIP.2006.312760

]. 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

]. 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

N. Michael, . Bleicher, W. Donald, and . Crowe, Anatole Beck Excursions into mathematics : The millennium edition, 2000.

]. J. Da-costa, C. Germain, and P. Baylou, Orientation difference statistics for texture description, Object recognition supported by user interaction for service robots, pp.652-655, 2002.
DOI : 10.1109/ICPR.2002.1044833

URL : https://hal.archives-ouvertes.fr/hal-00169906

G. John and . Daugman, Complete Discrete 2-D Gabor Transforms by Neural Networks for Image Analysis and Compression, IEEE Transactions on acoustics, speech ans signal processing, vol.36, pp.1169-1179, 1988.

]. S. Deans, The radon transform and some of its applications] Do. The finite ridgelet transform for image representation, IEEE Transactions on image processing, vol.12, pp.16-28, 1983.

]. D. Donoho and I. M. Johnstone, Threshold selection for wavelet shrinkage of noisy data, Proceedings of 16th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pp.24-25, 1994.
DOI : 10.1109/IEMBS.1994.412133

]. D. Donoho, De-noising by soft-thresholding, IEEE Transactions on Information Theory, vol.41, issue.3, pp.613-627, 1995.
DOI : 10.1109/18.382009

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.161.9704

]. C. Duchon, Lanczos Filtering in One and Two Dimensions, Journal of Applied Meteorology, vol.18, issue.8, pp.1016-1023, 1979.
DOI : 10.1175/1520-0450(1979)018<1016:LFIOAT>2.0.CO;2

A. Jerome, C. M. Feldman, G. Feldman, C. Falk, J. Grape et al., The Stanford Hand-Eye Project, IJCAI, pp.521-526, 1969.

]. W. 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

]. 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

]. S. Grgic, M. Grgic, and B. Zovko-cihlar, Performance analysis of image compression using wavelets, IEEE Transactions on Industrial Electronics, vol.48, issue.3, pp.682-695, 2001.
DOI : 10.1109/41.925596

]. A. Grossmann and J. Morel, Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape, SIAM Journal on Mathematical Analysis, vol.15, issue.4, pp.723-736, 1984.
DOI : 10.1137/0515056

H. John, R. Conway, and . Guy, The book of numbers, BIBLIOGRAPHIE, 1995.

H. Hou and H. Andrews, Cubic splines for image interpolation and digital filtering, IEEE Transactions on Acoustics, Speech and Signal Processing, vol.26, issue.6, pp.508-517, 1978.

[. Khouzani, K. , and S. Zadeh, Radon transform orientation estimation for rotation invariant texture analysis, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.27, issue.6, pp.1004-1008, 2005.
DOI : 10.1109/TPAMI.2005.126

]. N. Jayant and P. Noll, Digital coding of waveforms. Principles and applications to speech and video, Signal Processing, vol.9, issue.2, 1984.
DOI : 10.1016/0165-1684(85)90053-2

]. K. Jensen and D. Anastassiou, Subpixel edge localization and the interpolation of still images, IEEE Transactions on Image Processing, vol.4, issue.3, pp.285-295, 1995.
DOI : 10.1109/83.366477

J. Hao and C. Moloney, A new direction adaptive scheme for image interpolation, ICIP, vol.33, pp.369-372, 2002.

]. R. Keys, Cubic convolution interpolation for digital image processing, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.29, issue.6, pp.1153-1160, 1981.
DOI : 10.1109/TASSP.1981.1163711

]. T. Lehmann, C. Gonner, and K. Spitzer, Survey: interpolation methods in medical image processing, IEEE Transactions on Medical Imaging, vol.18, issue.11, pp.1049-1075, 1999.
DOI : 10.1109/42.816070

X. Li and M. T. Orchard, New edge-directed interpolation, ICIP, vol.10, issue.10, pp.1521-1527, 2001.

]. F. Luisier, T. Blu, and M. Unser, A New SURE Approach to Image Denoising: Interscale Orthonormal Wavelet Thresholding, IEEE Transactions on Image Processing, vol.16, issue.3, pp.593-606, 2007.
DOI : 10.1109/TIP.2007.891064

]. 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, A wavelet tour of signal processing, 1999.

]. E. Lepennec-;-s and . Mallat, Sparse Geometric Image Representations With Bandelets, IEEE Transactions on image processing, vol.14, 2005.

]. S. Mallat and G. Peyre, A review of Bandlet methods for geometrical image representation, Numerical Algorithms, vol.15, issue.5, pp.205-234, 2007.
DOI : 10.1007/s11075-007-9092-4

URL : https://hal.archives-ouvertes.fr/hal-00359744

]. F. Meyer and R. R. Coifman, Adaptive directional image compression with oriented wavelets, Proceedings of 3rd IEEE International Conference on Image Processing, pp.601-604, 1996.
DOI : 10.1109/ICIP.1996.559568

]. F. Michelet, C. Germain, P. Baylou, J. P. Da, and C. , Local multiple orientation estimation: isotropic and recursive oriented network, Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004., pp.712-715, 2004.
DOI : 10.1109/ICPR.2004.1334281

URL : https://hal.archives-ouvertes.fr/hal-00167916

]. Michelet, J. Costa, O. Lavialle, Y. Berthoumieu, P. Baylou et al., Estimating local multiple orientations, Signal Processing, vol.87, issue.7, pp.1655-1669, 2007.
DOI : 10.1016/j.sigpro.2007.01.017

URL : https://hal.archives-ouvertes.fr/hal-00166478

]. B. Morse and D. Schwartzwald, Image magnification using level-set reconstruction, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001, pp.333-340, 2001.
DOI : 10.1109/CVPR.2001.990494

]. D. Muresan, Fast edge directed polynomial interpolation, IEEE International Conference on Image Processing 2005, pp.990-993, 2005.
DOI : 10.1109/ICIP.2005.1530224

E. Donald, R. Knuth, O. Graham, and . Patashnik, Concrete mathematics : A foundation for computer science, 1994.

]. P. Perona, Orientation diffusions, IEEE Transactions on Image Processing, vol.7, issue.3, pp.457-467, 1998.
DOI : 10.1109/83.661195

URL : http://authors.library.caltech.edu/2145/1/PERieeetip98.pdf

. Peyre, Géométrie multi-´ echelles pour les images et les textures, 2005.

]. G. Peyre and S. Mallat, Discrete bandelets with geometric orthogonal filters, IEEE International Conference on Image Processing 2005, pp.65-73, 2005.
DOI : 10.1109/ICIP.2005.1529688

URL : https://hal.archives-ouvertes.fr/hal-00365624

]. G. Peyre, Bandlet Toolbox, www.mathworks.com/matlabcentral/fileexchange, 2007.

]. S. Rahman, M. O. Ahmad, and M. N. Swamy, Bayesian Wavelet-Based Image Denoising Using the Gauss&#x2013;Hermite Expansion, IEEE Transactions on Image Processing, vol.17, issue.10, pp.1755-1771, 2008.
DOI : 10.1109/TIP.2008.2002163

. Br-ramesh and . Srinivasa, An algorithm for computing the discrete Radon transform with some applications, Fourth IEEE Region 10 International Conference TENCON, 1989.
DOI : 10.1109/TENCON.1989.176899

]. J. Starck, E. J. Candes, and D. L. Donoho, The curvelet transform for image denoising, IEEE Transactions on Image Processing, vol.11, issue.6, pp.670-684, 2002.
DOI : 10.1109/TIP.2002.1014998

]. J. Starck, J. Fadili, and F. Murtagh, The Undecimated Wavelet Decomposition and its Reconstruction, IEEE Transactions on Image Processing, vol.16, issue.2, pp.297-309, 2007.
DOI : 10.1109/TIP.2006.887733

URL : https://hal.archives-ouvertes.fr/hal-00080092

]. 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

]. M. Unser, A. Aldroubi, and M. Eden, Fast B-spline transforms for continuous image representation and interpolation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.13, issue.3, pp.277-285, 1991.
DOI : 10.1109/34.75515

]. M. Unser, A. Aldroubi, and M. Eden, B-spline signal processing. I. Theory, IEEE Transactions on Signal Processing, vol.41, issue.2, pp.821-833, 1993.
DOI : 10.1109/78.193220

]. M. Unser, Splines: a perfect fit for signal and image processing, IEEE Signal Processing Magazine, vol.16, issue.6, pp.22-38, 1999.
DOI : 10.1109/79.799930

. Van-reeth-2010a-]-e, P. Van-reeth, M. Bertolino, and . Nicolas, Procédé de détection d'orientation de contours, 2010.

. Van-reeth-2010b-]-e, P. Van-reeth, M. Bertolino, J. M. Nicolas, and . Chassery, Adaptive edge orientation analysis, Wavelet Applications in Industrial Processing VII, 2010.
DOI : 10.1117/12.838990

. Van-reeth-2011a-]-e, P. Van-reeth, M. Bertolino, and . Nicolas, Agrandissement d'image basé sur une carte directionnelle multirésolution. GRETSI, 2011.

. Van-reeth-2011b-]-e, P. Van-reeth, M. Bertolino, and . Nicolas, Image interpolation based on a multi-resolution directional map, Image Processing: Algorithms and Systems IX, 2011.
DOI : 10.1117/12.872371

]. V. Velisavljevic, B. Beferull-lozano, M. Vetterli, and P. L. Dragotti, Discrete multidirectional wavelet bases, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429), pp.1025-1033, 2003.
DOI : 10.1109/ICIP.2003.1247140

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.59.7753

]. V. Velisavljevic, 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

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.107.7518

]. J. Villasenor, B. Belzer, and J. Liao, Wavelet filter evaluation for image compression, IEEE Transactions on Image Processing, vol.4, issue.8, pp.1053-1060, 1995.
DOI : 10.1109/83.403412

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

]. , W. , and R. K. Ward, A New Orientation-Adaptive Interpolation Method, ICIP, vol.16, issue.4, pp.889-900, 2007.

]. Xiong, Y. Zhang, X. Sun, and F. Wu, Fast directional image interpolation with difference projection, 2009 IEEE International Conference on Multimedia and Expo, pp.81-84, 2009.
DOI : 10.1109/ICME.2009.5202441

]. E. Yeung, Image compression using wavelets, CCECE '97. Canadian Conference on Electrical and Computer Engineering. Engineering Innovation: Voyage of Discovery. Conference Proceedings, pp.241-244, 1997.
DOI : 10.1109/CCECE.1997.614834

]. Zhang-et-le-nan-xiaolin and . Wu, An edge-guided image interpolation algorithm via directional filtering and data fusion, IEEE Transactions on Image Processing, vol.15, issue.8, pp.2226-2238, 2006.
DOI : 10.1109/TIP.2006.877407

. Par-la-suite, Elle est basée sur l'utilisation d'un noyau d'interpolation isotrope (cubic-spline), qui est corrigée grâcè a un filtrage Gaussien localement orienté dans la direction des contours. Les régions ne contenant pas de contour sont préservées grâcè a la création d'un masque construitàconstruità partir de filtres de Gabor. Enfin, les résultats de notre interpolation sont comparéscomparésà des méthodes d'interpolation directionnelle récentes