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Sparse directional image representations using the discrete shearlet transform
Open accessAbstract
Abstract In spite of their remarkable success in signal processing applications, it is now widely acknowledged that traditional wavelets are not very effective in dealing multidimensional signals containing distributed discontinuities such as edges. To overcome this limitation, one has to use basis elements with much higher directional sensitivity and of various shapes, to be able to capture the intrinsic geometrical features of multidimensional phenomena. This paper introduces a new discrete multiscale directional representation called the discrete shearlet transform. This approach, which is based on the shearlet transform, combines the power of multiscale methods with a unique ability to capture the geometry of multidimensional data and is optimally efficient in representing images containing edges. We describe two different methods of implementing the shearlet transform. The numerical experiments presented in this paper demonstrate that the discrete shearlet transform is very competitive in denoising applications both in terms of performance and computational efficiency.
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Cites
The Laplacian pyramid as a compact image code
Burt, P., & Adelson, E. (1983) · IEEE Transactions on Communications · doi:10.1109/tcom.1983.1095851 · Cited by 6,077
Fast Discrete Curvelet Transforms
Candès, E., Demanet, L., Donoho, D., & Ying, L. (2006) · Multiscale Modeling & Simulation · doi:10.1137/05064182x · Cited by 2,573
Cited by
Yin, M., Liu, X., Liu, Y., & Chen, X. (2019) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/tim.2018.2838778 · Cited by 594
A review of multimodal medical image fusion techniques
Huang, B., Yang, F., Yin, M., Mo, X., & Zhong, C. (2020) · Computational and Mathematical Methods in Medicine · doi:10.1155/2020/8279342 · Cited by 220
Surface Defects Classification of Hot-Rolled Steel Strips Using Multi-directional Shearlet Features
Ashour, M. W., Khalid, F., Abdul Halin, A., Abdullah, L. N., & Darwish, S. H. (2019) · Arabian Journal for Science and Engineering · doi:10.1007/s13369-018-3329-5 · Cited by 77
Application of Shearlet transform to classification of surface defects for metals
Xu, K., Liu, S., & Ai, Y. (2015) · Image and Vision Computing · doi:10.1016/j.imavis.2015.01.001 · Cited by 55
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
- Easley, G., Labate, D., & Lim, W.-Q.
- Venue
- Applied and Computational Harmonic Analysis
- Publisher
- Elsevier BV
- Published
- 2008-07
- Volume
- 25
- Issue
- 1
- Pages
- 25-46
- ISSN
- 1063-5203 (ISSN-L)
- OpenAlex
- W2097061348
- Cited by
- 1,040
- References
- 2
- FWCI
- 20.07
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Easley, G., Labate, D., & Lim, W.-Q. (2008). Sparse directional image representations using the discrete shearlet transform. Applied and Computational Harmonic Analysis. https://doi.org/10.1016/j.acha.2007.09.003
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