Sparse multidimensional representation using shearlets

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 5914, Issue , 2005, Pages 1-9

  Labate, Demetrio ^a   Lim, Wang Q ^b   Kutyniok, Gitta ^c   Weiss, Guido ^b  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b WASHINGTON UNIVERSITY   (United States)

^c JUSTUS LIEBIG UNIVERSITY   (Germany)

Author keywords

Affine systems; Curvelets; Geometric image processing; Shearlets; Sparse representation; Wavelets

Indexed keywords

ALGORITHMS; FUNCTION EVALUATION; IMAGE PROCESSING; OPTICAL RESOLVING POWER; OSCILLATIONS;

AFFINE SYSTEMS; CURVELETS; GEOMETRIC IMAGE PROCESSING; SHEARLETS;

OPTICAL SYSTEMS;

EID: 30844463689     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.613494     Document Type: Conference Paper

References (17)

1. D. L. Donoho, M. Vetterli, R.A. DeVore, and I. Daubechies, Data compression and harmonic analysis, IEEE Trans. Inform. Th. 44 (1998), 2435-2476.
2. S. Mallat, A Wavelet Tour of Signal Processing, Academic Press, San Diego (1998).
3. J. P. Antoine, R. Murenzi, and P. Vandergheynst, Directional wavelets revisited: Cauchy wavelets and symmetry detection in patterns, Appl. Computat. Harmon. Anal. 6 (1999), 314-345.
4. N. Kingsbury, Complex wavelets for shift invariant analysis and filtering of signals, Appl. Computat. Harmon. Anal. 10 (2001), 234-253.
5. E.J. Candès and D.L. Donoho, Ridgelets: a key to higher-dimensional intermittency?, Phil. Trans. Royal Soc. London A 357 (1999), 2495-2509.
6. E.J. Candès and D.L. Donoho, Curvelets - a surprising effective nonadaptive representation for objects with edges, in: Curves and Surfaces, C. Rabut, A. Cohen and L.L. Schumaker (Eds.), Vanderbilt University Press, Nashville, 2000.
7. 2 singularities, Comm. Pure and Appl. Math. 56 (2004), 216-266.
8. M.N. Do and M. Vetterli, The contourlet transform: an efficient directional multiresolution image representation, to appear in: IEEE Transactions Image on Processing, 2005.
9. K. Guo, W-Q. Lim, D. Labate, G. Weiss and E. Wilson, Wavelets with composite dilations and their MRA properties, to appear in: Appl. Computat. Harmon. Anal.
10. G. Kutyniok and D. Labate, Resolution of the wavefront set using shearlets, preprint 2005.
11. E.J. Candès and D.L. Donoho, Continuous curvelet transform: I. Resolution of the wavefront set, to appear in: Appl. Comput. Harmon. Anal. 2005.
12. Y. Meyer, Ondelettes et Operateurs, I, Hermann, Paris (1990).
13. E.J. Candès and D.L. Donoho, Continuous curvelet transform: II. Discretization and frames, to appear in: Appl. Comput. Harmon. Anal. 2005.
14. K. Guo, W-Q. Lim, D. Labate, G. Weiss and E. Wilson, Wavelets with composite dilations, Electr. Res. Announc. of AMS 10 (2004), 78-87.
15. K. Guo, W-Q. Lim, D. Labate, G. Weiss and E. Wilson, The theory of wavelets with composite dilations, to appear in: Harmonic Analysis and Applications, C. Heil (ed.), Birkhäuser, Boston (2005).
16. W-Q. Lim, Wavelets with Composite Dilations, Ph.D. Thesis, Washington University in St. Louis, 2005.
17. D.D. Po and M.N. Do, Directional multiscale modeling of images using the contourlet transform, to appear in: IEEE Transactions Image on Processing, 2005.