The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Singularity detection and processing with wavelets
Abstract
The mathematical characterization of singularities with Lipschitz exponents is reviewed. Theorems that estimate local Lipschitz exponents of functions from the evolution across scales of their wavelet transform are reviewed. It is then proven that the local maxima of the wavelet transform modulus detect the locations of irregular structures and provide numerical procedures to compute their Lipschitz exponents. The wavelet transform of singularities with fast oscillations has a particular behavior that is studied separately. The local frequency of such oscillations is measured from the wavelet transform modulus maxima. It has been shown numerically that one- and two-dimensional signals can be reconstructed, with a good approximation, from the local maxima of their wavelet transform modulus. As an application, an algorithm is developed that removes white noises from signals by analyzing the evolution of the wavelet transform maxima across scales. In two dimensions, the wavelet transform maxima indicate the location of edges in images.>
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Cites
A Computational Approach to Edge Detection
Canny, J. (1986) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.1986.4767851 · Cited by 30,004
Marr, D., & Hildreth, E. (1980) · Proceedings of the Royal Society of London. Series B. Biological Sciences · doi:10.1098/rspb.1980.0020 · Cited by 6,510
The wavelet transform, time-frequency localization and signal analysis
Daubechies, I. (1990) · IEEE Transactions on Information Theory · doi:10.1109/18.57199 · Cited by 6,483
Cited by
Feature detection with automatic scale selection
Lindeberg, T. (1998) · International Journal of Computer Vision · doi:10.1023/a:1008045108935 · Cited by 2,541
Wavelet-based statistical signal processing using hidden Markov models
Crouse, M. S., Nowak, R. D., & Baraniuk, R. G. (1998) · IEEE Transactions on Signal Processing · doi:10.1109/78.668544 · Cited by 1,643
Multiresolution analysis for surfaces of arbitrary topological type
Lounsbery, M., DeRose, T. D., & Warren, J. (1997) · ACM Transactions on Graphics · doi:10.1145/237748.237750 · Cited by 760
Wavelet transform domain filters: a spatially selective noise filtration technique
Xu, Y., Weaver, J. B., Healy, D. M., & Lu, J. (1994) · IEEE Transactions on Image Processing · doi:10.1109/83.336245 · Cited by 747
Preece, S. J., Goulermas, J. Y., Kenney, L. P. J., & Howard, D. (2009) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2008.2006190 · Cited by 551
Metadata
- Authors
- Mallat, S., & Hwang, W. L.
- Venue
- IEEE Transactions on Information Theory
- Published
- 1992-03
- Volume
- 38
- Issue
- 2
- Pages
- 617-643
- ISSN
- 0018-9448 (ISSN-L)
- 1557-9654
- OpenAlex
- W2152328854
- Cited by
- 3,863
- References
- 3
- FWCI
- 76.21
- Type
- journal article
- Language
- en
- Open access
- closed
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- Mallat, S., & Hwang, W. L. (1992). Singularity detection and processing with wavelets. IEEE Transactions on Information Theory. https://doi.org/10.1109/18.119727
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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