Orthogonal bandelet bases for geometric images approximation

Communications on Pure and Applied Mathematics

Volumn 61, Issue 9, 2008, Pages 1173-1212

  Mallat, Stéphane ^a,b   Peyré, Gabriel ^b,c  

^a CMAP

^b UNIVERSITÉ PARIS DAUPHINE   (France)

^c CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 52349096502     PISSN: 00103640     EISSN: 00103640     Source Type: Journal    
DOI: 10.1002/cpa.20242     Document Type: Article

References (22)

1. 2 for the sparse representation of integral operators. SIAM J. Math. Anal. 24 (1993), no. 1, 246-262.
2. Bosking, W. H.; Zhang, Y.; Schofield, B.; Fitzpatrick, D. Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex. J. Neurosci. 17 (1997), no. 6, 2112-2127.
3. Breiman, L.; Friedman, J.; Olshen, R. A.; Stone, C. J. Classification and regression trees. Wadsworth Statistics/Probability Series. Wadsworth, Belmont, Calif., 1984.
4. 2 singularities. Comm. Pure Appl. Math. 57 (2004), no. 2, 219-266.
5. Claypoole, R. L.; Davis, G. M.; Sweldens, W.; Baraniuk, R. G. Nonlinear wavelet transforms for image coding via lifting. IEEE Trans. Image Process. 12 (2003), no. 12, 1449-1459.
6. Cohen, A.; Daubechies, I.; Vial, P. Wavelets on the interval and fast wavelet transforms. Appl. Comput. Harmon. Anal. 1 (1993), no. 1, 54-81.
7. DeAngelis G. C.; Ohzawa, I.; Freeman, R. D. Receptive-field dynamics in the central visual pathways. Trends Neurosci. 18 (1995), no. 10, 451-458.
8. Do, M. N.; Vetterli, M. The contourlet transform: an efficient directional multiresolution image representation. IEEE Trans. Image Process. 14 (2005), no. 12, 2091-2106.
9. Donoho, D. L. Wedgelets: nearly-minimax estimation of edges. Ann. Statist. 27 (1999), no. 3, 859-897.
10. Donoho, D. L. Counting bits with Kolmogorov and Shannon. Technical Report No. 2000-38, Department of Statistics, Stanford University, December 2000. Available online at: http:// www-stat.Stanford.edu/reports/abstracts/00-38.ps
11. Dragotti, P. L.; Vetterli, M. Wavelet footprints: theory, algorithms, and applications. IEEE Trans. Signal Process. 51 (2003), no. 5, 1306-1323.
12. Field, D. J.; Hayes, A.; Hess, R. F. Contour integration by the human visual system: evidence for a local "association field." Vision Res. 33 (1993), no. 2, 173-193.
13. Hubel, D. H.; Wiesel, T. N. Receptive fields and functional architecture of monkey striate cortex. J. Physiol. 195 (1968), no. 1, 215-243.
14. Le Pennec, E.; Mallat, S. Bandelet image approximation and compression. SIAM Multiscale Modeling and Simulation 4 (2005), no. 3, 992-1039.
15. Lee, T. S. Computations in the early visual cortex. J. Physiol. Paris 97 (2003), no. 2-3, 121-139.
16. Mallat, S. A wavelet tour of signal processing. Academic Press, San Diego, 1998.
17. Matei, B.; Cohen, A. Nonlinear subdivison schemes: applications to image processing. Tutorials on multiresolution in geometric modelling, 93-97. Springer New York, Secaucus, N.J., 2002.
18. Meyer, Y. Wavelets and operators. Cambridge Studies in Advanced Mathematics, 37. Cambridge University Press, Cambridge, 1992.
19. Peyré, G. Bandelets toolbox. Available online at: http://www.mathworks.com/matlabcentral/fileexchange/loadAuthor.do?objectType= author& objectId=1094083
20. Peyré, G.; Mallat, S. Surface compression with geometric bandelets. ACM Transactions on Graphics (TOG) 24 (2005), no. 3, 601-608.
21. Shukla, R.; Dragotti, P. L.; Do, M. N.; Vetterli, M. Rate-distortion optimized tree-structured compression algorithms for piecewise polynomial images. IEEE Trans. Image Process. 14 (2005), no. 3, 343-359.
22. Wakin, M. B.; Romberg, J. K.; Choi, H.; Baraniuk, R. G. Wavelet-domain approximation and compression of piecewise smooth images. IEEE Trans. Image Process. 15 (2006), no. 5, 1071-1087.