Free Access
Issue
Math. Model. Nat. Phenom.
Volume 8, Number 1, 2013
Harmonic analysis
Page(s) 60 - 74
DOI https://doi.org/10.1051/mmnp/20138104
Published online 28 January 2013
  1. J. Bobin, J.-L. Starck, M.J. Fadili, Y. Moudden, D.L. Donoho. Morphological component analysis : an adaptive thresholding strategy. IEEE Trans. Image Process. 16 (11) (2007), 2675–2681. [NASA ADS] [CrossRef] [MathSciNet] [PubMed]
  2. E. J. Candès, L. Demanet, D. Donoho, L. Ying. Fast discrete curvelet transforms. Multiscale Model. Simul. 5 (2006), 861–899. [CrossRef]
  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]
  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]
  5. S. S. Chen, D. L. Donoho, M. A. Saunders. Atomic decomposition by basis pursuit. SIAM Rev. 43 (1) (2001), 129–159. [NASA ADS] [CrossRef] [MathSciNet]
  6. I. Daubechies, M. Defrise, C. De Mol. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Comm. Pure Appl. Math. 57 (2004), 1413–1457. [CrossRef] [MathSciNet]
  7. D. L. Donoho. Denoising by soft thresholding. IEEE Trans. Inf. Theory, 41 (3) (1995), 613–627. [CrossRef] [MathSciNet]
  8. D. L. Donoho. Sparse components of images and optimal atomic decomposition. Constr. Approx. 17 (2001), 353–382. [CrossRef] [MathSciNet]
  9. D. L. Donoho. Wedgelets : nearly-minimax estimation of edges. Annals of Statistics, 27 (1999), 859–897. [CrossRef]
  10. D. L. Donoho, I. M. Johnstone. Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81 (3) (1994), 425–455. [CrossRef] [MathSciNet]
  11. D. L. Donoho, I. M. Johnstone. Adapting to unknown smoothness via wavelet shrinkage. J. Amer. Statist. Assoc. 90 (1995), 1200–1224. [CrossRef] [MathSciNet]
  12. D. L. Donoho, I. M. Johnstone, G. Kerkyacharian, D. Picard. Wavelet shrinkage. Asymptopia. J. Roy. Statist. Soc. B, 57 (2) (1995), 301–337.
  13. G. R. Easley, D. Labate, F. Colonna. Shearlet-based total variation diffusion for denoising. IEEE Trans. Image Proc. 18 (2) (2009), 260–268. [CrossRef]
  14. 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]
  15. M. Elad. Sparse and Redundant Representations : From Theory to Applications in Signal and Image Processing. Springer, New York, NY, 2010.
  16. M. Elad, P. Milanfar, R. Rubinstein. Analysis Versus Synthesis in Signal Priors. Inverse Problems, 23 (3) (2007), 947–968. [NASA ADS] [CrossRef]
  17. 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), 189–201.
  18. K. Guo, D. Labate. Optimally Sparse Multidimensional Representation using Shearlets. SIAM J. Math. Anal.. 9 (2007), 298–318. [CrossRef] [MathSciNet]
  19. K. Guo, D. Labate. Optimally sparse 3D approximations using shearlet representations. Electron. Res. Announc. Math. Sci. 17 (2010), 126–138.
  20. 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]
  21. K. Guo, D. Labate. The Construction of Smooth Parseval Frames of Shearlets. Math. Model. Nat. Phenom. 8 (1) (2013), 3255.
  22. X. Huo. Sparse Image Representation Via Combined Transforms, Ph.D. Thesis, Stanford University, 1999.
  23. G. Kutyniok. Clustered sparsity and separation of cartoon and texture, preprint (2012).
  24. 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.
  25. Y. Lu, M. N. Do. Multidimensional directional filter banks and surfacelets, IEEE Trans. Image Process., 16 (4) (2007), 918–931. [CrossRef] [MathSciNet] [PubMed]
  26. F. Malgouyres. Minimizing the total variation under a general convex constraint for image restoration. IEEE Trans. Signal Process. 11 (12) (2002), 1450–1456.
  27. S. Mallat. A Wavelet Tour of Signal Processing.Third Edition : The Sparse Way, Academic Press, San Diego, CA, 2008.
  28. F. G. Meyer, A. Z. Averbuch, R. Coifman. Multi-layered image representation : Application to image compression, IEEE Trans. Image Process. 11(6) (1998), 1072–1080. [CrossRef]
  29. P. S. Negi, D. Labate. 3D discrete shearlet transform and video processing, IEEE Trans. Image Process. 21(6) (2012), 944–2954.
  30. V. M. Patel, G. R. Easley, R. Chellappa, Component-based restoration of speckled images, Proceedings 18th IEEE International Conference on Image Processing (ICIP), 2011.
  31. J. L. Starck, M. Elad, D.L. Donoho. Image decomposition via the combination of sparse representations and a variational approach, IEEE Trans. Image Process. 14(10) (2005), 1570–1582. [NASA ADS] [CrossRef] [MathSciNet] [PubMed]
  32. J. L. Starck, F. Murtagh, A. Bijaoui. Multiresolution support applied to image filtering and restoration, Graphic. Models Image Process. 57 (1995), 420–431. [CrossRef]
  33. J. L. Starck, F. Murtagh, J. M. Fadili. Sparse Image and Signal Processing, Cambridge University Press, New York, NY, 2010.
  34. A. Woiselle, J. L. Starck, J. M. Fadili. 3-D Data denoising and inpainting with the Low-Redundancy Fast Curvelet Transform, J. Math. Imaging Vis. 39(2) (2011), 121–139. [CrossRef]

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