Free Access
Issue
Math. Model. Nat. Phenom.
Volume 8, Number 1, 2013
Harmonic analysis
Page(s) 82 - 105
DOI https://doi.org/10.1051/mmnp/20138106
Published online 28 January 2013
  1. E. J. Candès, L. Demanet. The curvelet representation of wave propagators is optimally sparse. Comm. Pure Appl. Math. 58 (2005), 1472–1528. [CrossRef] [MathSciNet] [Google Scholar]
  2. E. J. Candès, L. Demanet, D. Donoho, L. Ying. Fast Discrete Curvelet Transforms. Multiscale Model. Simul. 5 (2006), 861–899. [CrossRef] [Google Scholar]
  3. E. J. Candès, D. L. Donoho. Ridgelets : the key to high dimensional intermittency?. Philosophical Transactions of the Royal Society of London A 357 (1999), 2495–2509. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  4. E. J. Candès, D. L. Donoho. New tight frames of curvelets and optimal representations of objects with C2 singularities. Comm. Pure Appl. Math. 57 (2004), 219–266. [CrossRef] [Google Scholar]
  5. F. Colonna, G. Easley, K. Guo, D. Labate. Radon Transform Inversion using the Shearlet Representation. Appl. Comput. Harmon. Anal. 29 (2) (2010), 232–250. [CrossRef] [Google Scholar]
  6. S. Dahlke, G. Kutyniok, P. Maass, C. Sagiv, H.-G. Stark, G. Teschke. The uncertainty principle associated with the continuous shearlet transform. Int. J. Wavelets Multiresolut. Inf. Process. 6 (2008), 157–181. [CrossRef] [MathSciNet] [Google Scholar]
  7. M. N. Do, M. Vetterli. The contourlet transform : an efficient directional multiresolution image representation. IEEE Trans. Image Process. 14 (2005), 2091–2106. [CrossRef] [PubMed] [Google Scholar]
  8. D. L. Donoho. Wedgelets : Nearly-minimax estimation of edges. Annals of Statistics, 27 (1999), 859–897. [CrossRef] [Google Scholar]
  9. G. R. Easley, D. Labate, F. Colonna. Shearlet-Based Total Variation Diffusion for Denoising. IEEE Trans. Image Proc. 18 (2) (2009), 260–268. [CrossRef] [Google Scholar]
  10. G. R. Easley, D. Labate, W. Lim. Sparse Directional Image Representations using the Discrete Shearlet Transform. Appl. Comput. Harmon. Anal. 25 (1) (2008), 25–46. [CrossRef] [Google Scholar]
  11. P. Grohs. Tree Approximation with anisotropic decompositions. Appl. Comput. Harmon. Anal. 33(1) (2012), 44–57. [CrossRef] [Google Scholar]
  12. P. Grohs. Bandlimited Shearlet Frames with nice Duals. SAM Report 2011-55, ETH Zurich, July 2011. [Google Scholar]
  13. K. Guo, G. Kutyniok, D. Labate. Sparse Multidimensional Representations using Anisotropic Dilation and Shear Operators in : Wavelets and Splines, G. Chen and M. Lai (eds.), Nashboro Press, Nashville, TN (2006), pp. 189–201. [Google Scholar]
  14. K. Guo, D. Labate. Optimally Sparse Multidimensional Representation using Shearlets. SIAM J. Math. Anal. 9 (2007), 298–318 [CrossRef] [MathSciNet] [Google Scholar]
  15. K. Guo, D. Labate. Representation of Fourier Integral Operators using Shearlets. J. Fourier Anal. Appl. 14 (2008), 327–371 [CrossRef] [Google Scholar]
  16. K. Guo, D. Labate. Characterization and analysis of edges using the continuous shearlet transform. SIAM J. Imag. Sci. 2 (2009), 959–986. [CrossRef] [Google Scholar]
  17. K. Guo, D. Labate. Optimally sparse 3D approximations using shearlet representations. Electron. Res. Announc. Math. Sci. 17 (2010), 126–138. [Google Scholar]
  18. K. Guo, D. Labate. Optimally sparse representations of 3D Data with C2 surface singularities using Parseval frames of shearlets. SIAM J Math. Anal. 44 (2012), 851–886. [CrossRef] [MathSciNet] [Google Scholar]
  19. K. Guo, D. Labate, W.-Q. Lim. Edge analysis and identification using the Continuous Shearlet Transform. Appl. Comput. Harmon. Anal. 27 (2009), 24–46. [CrossRef] [Google Scholar]
  20. K. Guo, D. Labate, W.-Q Lim, G. Weiss, E. Wilson. Wavelets with composite dilations. Electron. Res. Announc. Amer. Math. Soc. 10 (2004), 78–87. [CrossRef] [MathSciNet] [Google Scholar]
  21. K. Guo, D. Labate, W-Q. Lim, G. Weiss, E. Wilson. The theory of wavelets with composite dilations. in : Harmonic Analysis and Applications, C. Heil (ed.), Birkhäuser, Boston, MA, 2006. [Google Scholar]
  22. K. Guo, W-Q. Lim, D. Labate, G. Weiss, E. Wilson. Wavelets with composite dilations and their MRA properties. Appl. Computat. Harmon. Anal. 20 (2006), 231–249. [CrossRef] [Google Scholar]
  23. B. Han. Pairs of frequency-based nonhomogeneous dual wavelet frames in the distribution space. Appl. Comput. Harmon. Anal. 29 (2010), 330–353. [CrossRef] [Google Scholar]
  24. B. Han. Nonhomogeneous wavelet systems in high dimensions. Appl. Comput. Harmon. Anal. 32 (2012), 169–196. [CrossRef] [Google Scholar]
  25. R. Houska. The nonexistence of shearlet scaling functions. Appl. Comput Harmon. Anal. 32 (1) (2012), 28–44. [CrossRef] [Google Scholar]
  26. P. Kittipoom, G. Kutyniok, W.-Q Lim. Construction of compactly supported shearlet frames. Constr. Approx., to appear (2012). [Google Scholar]
  27. G. Kutyniok. Sparsity Equivalence of Anisotropic Decompositions. preprint (2012). [Google Scholar]
  28. G. Kutyniok, D. Labate. Resolution of the wavefront set using continuous shearlets. Trans. Amer. Math. Soc. 361 (2009), 2719–2754. [CrossRef] [MathSciNet] [Google Scholar]
  29. G. Kutyniok, W.-Q. Lim. Compactly supported shearlets are optimally sparse. J. Approx. Theory 163 (2011), 1564–1589. [CrossRef] [MathSciNet] [Google Scholar]
  30. G. Kutyniok, T. Sauer. Adaptive Directional Subdivision Schemes and Shearlet Multiresolution Analysis. SIAM J. Math. Anal. 41 (2009), 1436–1471. [CrossRef] [MathSciNet] [Google Scholar]
  31. D. Labate, W.-Q Lim, G. Kutyniok, G. Weiss. Sparse multidimensional representation using shearlets. in Wavelets XI, edited by M. Papadakis, A. F. Laine, and M. A. Unser, SPIE Proc. 5914 (2005), SPIE, Bellingham, WA, 2005, 254–262. [Google Scholar]
  32. Y. Meyer, R. Coifman. Wavelets, Calderón-Zygmund Operators and Multilinear Operators. Cambridge Univ. Press, Cambridge, 1997. [Google Scholar]
  33. P. S. Negi, D. Labate. 3D Discrete Shearlet Transform and Video Processing. IEEE Trans. Image Process. 21 (6) (2012), 2944–2954. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  34. V.M. Patel, G. Easley, D. M. Healy. Shearlet-based deconvolution. IEEE Trans. Image Process. 18 (12) (2009), 2673-2685 [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  35. S. Yi, D. Labate, G. R. Easley, H. Krim. A Shearlet approach to Edge Analysis and Detection. IEEE Trans. Image Process 18 (5) (2009), 929–941. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]

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