Sparse directional image representations using the discrete shearlet transform

Antoine, 1999, Directional wavelets revisited: Cauchy wavelets and symmetry detection in patterns, Appl. Comput. Harmon. Anal., 6, 314, 10.1006/acha.1998.0255

A. Averbuch, R. Coifman, D. Donoho, M. Israeli, Y. Shkolnisky, Fast slant stack: A notion of Radon transform for data in a Cartesian grid which is rapidly computible, algebraically exact, geometrically faithful and invertible, SIAM J. Sci. Comput. (2007), in press

Bamberger, 1992, A filter bank for directional decomposition of images: Theory and design, IEEE Trans. Signal Process., 40, 882, 10.1109/78.127960

Burt, 1983, The Laplacian pyramid as a compact image code, IEEE Trans. Commun., 31, 532, 10.1109/TCOM.1983.1095851

Candès, 2006, Fast discrete curvelet transforms, SIAM Multiscale Model. Simul., 5, 861, 10.1137/05064182X

Candès, 1999, Ridgelets: A key to higher-dimensional intermittency?, Philos. Trans. R. Soc. London A, 357, 2495, 10.1098/rsta.1999.0444

Candès, 2004, New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities, Comm. Pure Appl. Math., 56, 216

Coifman, 1995, Translation invariant de-noising, 125

Coifman, 1997, Brushlets: A tool for directional image analysis and image compression, Appl. Comput. Harmon. Anal., 5, 147

Colonna, 2005, Generalized discrete Radon transforms and their use in the ridgelet transform, J. Math. Imaging Vision, 23, 145, 10.1007/s10851-005-6463-0

Cunha, 2005, The non-subsampled contourlet transform: Theory, design, and applications, IEEE Trans. Image Process., 15, 3089

Do, 2005, The contourlet transform: An efficient directional multiresolution image representation, IEEE Trans. Image Process., 14, 2091, 10.1109/TIP.2005.859376

Donoho, 2001, Sparse components of images and optimal atomic decomposition, Constr. Approx., 17, 353, 10.1007/s003650010032

Donoho, 1998, Data compression and harmonic analysis, IEEE Trans. Inform. Theory, 44, 2435, 10.1109/18.720544

Donoho, 1994, Ideal spatial adaptation via wavelet shrinkage, Biometrica, 81, 425, 10.1093/biomet/81.3.425

G.R. Easley, C.A. Berenstein, D.M. Healy Jr., Deconvolution in a ridgelet and curvelet domain, in: Independent Component Analysis, Wavelets, Unsupervised Smart Sensors, and Neural Networks III, Proc. of SPIE, vol. 5818, 2005

Falzon, 1998, Analysis of low bit rate image transform coding, IEEE Trans. Image Process., 46, 1027, 10.1109/78.668554

K. Guo, G. Kutyniok, D. Labate, Sparse multidimensional representations using anisotropic dilation and shear operators, in: G. Chen, M. Lai, (Eds.), Wavelets and Splines: Athens 2005, Proceedings of the International Conference on the Interactions between Wavelets and Splines, Athens, GA, May 16–19, 2005

Guo, 2007, Optimally sparse multidimensional representation using shearlets, SIAM J. Math. Anal., 39, 298, 10.1137/060649781

Guo, 2004, Wavelets with composite dilations, Electron. Res. Announc. Amer. Math. Soc., 10, 78, 10.1090/S1079-6762-04-00132-5

Guo, 2006, The theory of wavelets with composite dilations, 231

Guo, 2006, Wavelets with composite dilations and their MRA properties, Appl. Comput. Harmon. Anal., 20, 231, 10.1007/0-8176-4504-7_11

Hernández, 1996

Hörmander, 2003

Kingsbury, 2001, Complex wavelets for shift invariant analysis and filtering of signals, Appl. Comput. Harmon. Anal., 10, 234, 10.1006/acha.2000.0343

Kryshtal, 2006, Compactly supported wavelets with composite dilations, J. Geom. Anal., 17, 87

Labate, 2005, Sparse multidimensional representation using shearlets, vol. 5914

Lang, 1996, Noise reduction using an undecimated discrete wavelet transform, Signal Process. Newslett., 3, 10, 10.1109/97.475823

Le Pennec, 2005, Sparse geometric image representations with bandelets, IEEE Trans. Image Process., 14, 423, 10.1109/TIP.2005.843753

W. Lim, Wavelets with composite dilations, Ph.D. thesis, Dept. Mathematics, Washington University in St. Louis, St. Louis, MO, 2006

Lu, 2005, Multidimensional directional filter banks and surfacelets, IEEE Trans. Image Process., 16, 918

Mallat, 1998

Po, 2006, Directional multiscale modeling of images using the contourlet transform, IEEE Trans. Image Process., 15, 1610, 10.1109/TIP.2006.873450

Sendur, 2002, Bivariance shrinkage with local variance estimator, IEEE Signal Process. Lett., 9, 438, 10.1109/LSP.2002.806054

Starck, 2002, The curvelet transform for image denoising, IEEE Trans. Image Process., 11, 670, 10.1109/TIP.2002.1014998