The DOI matches its Crossref record; 12 of the 12 references it cites were found in a registry or an index.
Sparse multidimensional representation using shearlets
Abstract
In this paper we describe a new class of multidimensional representation systems, called shearlets. They are obtained by applying the actions of dilation, shear transformation and translation to a fixed function, and exhibit the geometric and mathematical properties, e.g., directionality, elongated shapes, scales, oscillations, recently advocated by many authors for sparse image processing applications. These systems can be studied within the framework of a generalized multiresolution analysis. This approach leads to a recursive algorithm for the implementation of these systems, that generalizes the classical cascade algorithm.
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Cites
A Wavelet Tour of Signal Processing
(1999) · Elsevier eBooks · doi:10.1016/b978-0-12-466606-1.x5000-4 · Cited by 16,227
The contourlet transform: an efficient directional multiresolution image representation
Do, M. N., & Vetterli, M. (2005) · IEEE Transactions on Image Processing · doi:10.1109/tip.2005.859376 · Cited by 3,952
Complex Wavelets for Shift Invariant Analysis and Filtering of Signals
Kingsbury, N. (2001) · Applied and Computational Harmonic Analysis · doi:10.1006/acha.2000.0343 · Cited by 1,675
New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities
Candès, E. J., & Donoho, D. L. (2004) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.10116 · Cited by 1,545
Curvelets: A Surprisingly Effective Nonadaptive Representation for Objects with Edges
Candès, E. J., & Donoho, D. L. (2000) · Cited by 1,330
Ridgelets: a key to higher-dimensional intermittency?
Candès, E. J., & Donoho, D. L. (1999) · Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences · doi:10.1098/rsta.1999.0444 · Cited by 893
Directional multiscale modeling of images using the contourlet transform
Po, D. D.-Y., & Do, M. N. (2006) · IEEE Transactions on Image Processing · doi:10.1109/tip.2006.873450 · Cited by 576
Data compression and harmonic analysis
Donoho, D. L., Vetterli, M., DeVore, R. A., & Daubechies, I. (1998) · IEEE Transactions on Information Theory · doi:10.1109/18.720544 · Cited by 432
Candès, E. J., & Donoho, D. L. (2005) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2005.02.003 · Cited by 320
Wavelets with composite dilations and their MRA properties
Guo, K., Labate, D., Lim, W.-Q., Weiss, G., & Wilson, E. (2006) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2005.07.002 · Cited by 210
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Cited by
Fast Discrete Curvelet Transforms
Candès, E., Demanet, L., Donoho, D., & Ying, L. (2006) · Multiscale Modeling & Simulation · doi:10.1137/05064182x · Cited by 2,573
Double Sparsity: Learning Sparse Dictionaries for Sparse Signal Approximation
Rubinstein, R., Zibulevsky, M., & Elad, M. (2010) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2009.2036477 · Cited by 616
Surface defect identification of aluminium strips with non-subsampled shearlet transform
Liu, X., Xu, K., Zhou, P., Zhou, D., & Zhou, Y. (2020) · Optics and Lasers in Engineering · doi:10.1016/j.optlaseng.2019.105986 · Cited by 24
Metadata
- Authors
- Labate, D., Lim, W.-Q., Kutyniok, G., & Weiss, G.
- Venue
- SPIE Proceedings
- Publisher
- SPIE
- Published
- 2005-08-18
- Volume
- 5914
- Pages
- 59140U
- ISSN
- 0277-786X (ISSN-L)
- OpenAlex
- W2073996439
- Cited by
- 455
- References
- 12
- FWCI
- 14.59
- Type
- conference paper
- Language
- en
- Open access
- closed
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