Compactly supported shearlets

Springer Proceedings in Mathematics

Volumn 13, Issue , 2012, Pages 163-186

  Kutyniok, Gitta ^a   Lemvig, Jakob ^b   Lim, Wang Q ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPIC FEATURES; COMPACTLY SUPPORTED; FAST DECOMPOSITION; GENERALIZED MODELS; PARABOLIC SCALING; PIECE-WISE; PRECISE CONTROL; SCALINGS; SHEARLETS; SPARSE APPROXIMATIONS; TRANSLATION OPERATOR; WAVEFRONT SETS; WAVELET SYSTEMS;

APPROXIMATION THEORY;

EID: 84869772787     PISSN: 21905614     EISSN: 21905622     Source Type: Conference Proceeding    
DOI: 10.1007/978-1-4614-0772-0_10     Document Type: Conference Paper

References (40)

1. J. P. Antoine, P. Carrette, R. Murenzi, and B. Piette, Image analysis with two-dimensional continuous wavelet transform, Signal Process. 31 (1993), 241-272.
2. R. H. Bamberger and M. J. T. Smith, A filter bank for the directional decomposition of images: theory and design, IEEE Trans. Signal Process. 40 (1992), 882-893.
3. E. J. Candés, L. Demanet, D. Donoho, L. Ying, Fast discrete curvelet transforms, Multiscale Model. Simul. 5 (2006), 861-899.
4. E. J. Candés and D. L. Donoho, Curvelets-a suprisingly effective nonadaptive representation for objects with edges, in Curve and Surface Fitting: Saint-Malo 1999, edited by A. Cohen, C. Rabut, and L. L. Schumaker, Vanderbilt University Press, Nashville, TN, 2000.
5. 2 singularities, Comm. Pure and Appl. Math. 56 (2004), 216-266.
6. S. Dahlke, G. Kutyniok, G. Steidl, and G. Teschke, Shearlet coorbit spaces and associated Banach frames, Appl. Comput. Harmon. Anal. 27 (2009), 195-214.
7. S. Dahlke, G. Kutyniok, P. Maass, C. Sagiv, H.-G. Stark, and G. Teschke, The uncertainty principle associated with the continuous shearlet transform, Int. J. Wavelets Multiresolut. Inf. Process. 6 (2008), 157-181.
8. S. Dahlke, G. Steidl, and G. Teschke, The continuous shearlet transform in arbitrary space dimensions, J. Fourier Anal. Appl. 16 (2010), 340-364.
9. S. Dahlke and G. Teschke, The continuous shearlet transform in higher dimensions: variations of a theme, in Group Theory: Classes, Representation and Connections, and Applications, edited by C. W. Danellis, Math. Res. Develop., Nova Publishers, 2010, 167-175.
10. M. N. Do and M. Vetterli, The contourlet transform: an efficient directional multiresolution image representation, IEEE Trans. Image Process. 14 (2005), 2091-2106.
11. D. L. Donoho, Sparse components of images and optimal atomic decomposition, Constr. Approx. 17 (2001), 353-382.
12. D. L. Donoho and G. Kutyniok, Geometric separation using a wavelet-shearlet dictionary, SampTA'09 (Marseille, France, 2009), Proc., 2009.
13. D. L. Donoho and G. Kutyniok, Microlocal analysis of the geometric separation problem, preprint.
14. D. L. Donoho, G. Kutyniok, M. Shahram, and X. Zhuang, A rational design of a digital shearlet transform, preprint.
15. D. L. Donoho, A. Maleki, M. Shahram, V. Stodden, and I. Ur-Rahman, Fifteen years of reproducible research in computational harmonic analysis, Comput. Sci. Engrg. 11 (2009), 8-18.
16. G. Easley, D. Labate, and W.-Q Lim, Sparse directional image representations using the discrete shearlet transform, Appl. Comput. Harmon. Anal. 25 (2008), 25-46.
17. R. Eslami and H. Radha, A new family of nonredundant transforms using hybrid wavelets and directional filter banks, IEEE Trans. Image Process. 16 (2007), 1152-1167.
18. P. Grohs, Continuous shearlet frames and resolution of the wavefront set, Monatsh. Math., to appear. DOI: 10.1007/s00605-010-0264-2
19. P. Grohs, Continuous shearlet tight frames, J. Fourier Anal. Appl., 17 (2011), 506-518.
20. K. Guo, G. Kutyniok, and D. Labate, Sparse multidimensional representations using anisotropic dilation and shear operators, in Wavelets and Splines (Athens, GA, 2005), Nashboro Press, Nashville, TN, 2006, 189-201.
21. K. Guo and D. Labate, Optimally sparse multidimensional representation using shearlets, SIAM J. Math Anal. 39 (2007), 298-318.
22. K. Guo and D. Labate, Analysis and detection of surface discontinuities using the 3D continuous shearlet transform, Appl. Comput. Harmon. Anal. 30 (2011), 231-242.
23. K. Guo, D. Labate, W.-Q Lim, G. Weiss, and E. Wilson, Wavelets with composite dilations, Electron. Res. Announc. Amer. Math. Soc. 10 (2004), 78-87.
24. K. Guo, D. Labate, W.-Q Lim, G. Weiss, and E. Wilson, The theory of wavelets with composite dilations, Harmonic analysis and applications, Appl. Numer. Harmon. Anal., Birkhäuser Boston, Boston, MA, 2006, 231-250.
25. K. Guo, W.-Q Lim, D. Labate, G. Weiss, and E. Wilson, Wavelets with composite dilations and their MRA properties, Appl. Comput. Harmon. Anal. 20 (2006), 220-236.
26. B. Han, G. Kutyniok, and Z. Shen. A unitary extension principle for shearlet systems, SIAM J. Numer. Anal., to appear.
27. P. Kittipoom, G. Kutyniok, and W.-Q Lim, Construction of compactly supported shearlet frames, Constr. Approx., to appear.
28. P. Kittipoom, G. Kutyniok, and W.-Q Lim, Irregular shearlet frames: Geometry and approximation properties, J. Fourier Anal. Appl. 17 (2011), 604-639.
29. G. Kutyniok and D. Labate, Construction of regular and irregular shearlets, J. Wavelet Theory and Appl. 1 (2007), 1-10.
30. G. Kutyniok and D. Labate, Resolution of the wavefront set using continuous shearlets, Trans. Amer. Math. Soc. 361 (2009), 2719-2754.
31. α singularities, preprint.
32. G. Kutyniok and W.-Q Lim, Compactly supported shearlets are optimally sparse, J. Approx. Theory 163 (2011), 1564-1589.
33. G. Kutyniok and W.-Q Lim, Image separation using shearlets, in; Curves and Surfaces (Avignon, France, 2010), Lecture Notes in Computer Science, Springer, to appear.
34. G. Kutyniok and W.-Q Lim, Shearlets on bounded domains, in Approximation Theory XIII (San Antonio, TX, 2010), Springer, 13 (2012).
35. G. Kutyniok and T. Sauer, Adaptive directional subdivision schemes and shearlet multiresolution analysis, SIAM J. Math. Anal. 41 (2009), 1436-1471.
36. G. Kutyniok, M. Shahram, and D. L. Donoho, Development of a digital shearlet transform based on pseudo-polar FFT, in Wavelets XIII, edited by V. K. Goyal, M. Papadakis, D. Van De Ville, SPIE Proc. 7446, SPIE, Bellingham, WA, 2009, 7446-12.
37. D. Labate, W.-Q Lim, G. Kutyniok, and G. Weiss. Sparse multidimensional representation using shearlets, in Wavelets XI, edited by M. Papadakis, A. F. Laine, and M. A. Unser, SPIE Proc. 5914, SPIE, Bellingham, WA, 2005, 254-262
38. W.-Q Lim, The discrete shearlet transform: A new directional transform and compactly supported shearlet frames, IEEE Trans. Image Process. 19 (2010), 1166-1180.
39. E. L. Pennec and S. Mallat, Sparse geometric image representations with bandelets, IEEE Trans. Image Process. 14 (2005), 423-438.
40. E. P. Simoncelli, W. T. Freeman, E. H. Adelson, D. J. Heeger, Shiftable multiscale transforms, IEEE Trans. Inform. Theory 38 (1992), 587-607.