The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
A theory for multiresolution signal decomposition: the wavelet representation
Abstract
Multiresolution representations are effective for analyzing the information content of images. The properties of the operator which approximates a signal at a given resolution were studied. It is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2/sup j/ (where j is an integer) can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions. In L/sup 2/(R), a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi (x). This decomposition defines an orthogonal multiresolution representation called a wavelet representation. It is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters. Wavelet representation lies between the spatial and Fourier domains. For images, the wavelet representation differentiates several spatial orientations. The application of this representation to data compression in image coding, texture discrimination and fractal analysis is discussed.>
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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
Koenderink, J. J. (1984) · Biological Cybernetics · doi:10.1007/bf00336961 · Cited by 2,452
Textons, the elements of texture perception, and their interactions
Julesz, B. (1981) · Nature · doi:10.1038/290091a0 · Cited by 1,703
Cited by
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
Sparse coding with an overcomplete basis set: A strategy employed by V1?
Olshausen, B. A., & Field, D. J. (1997) · Vision Research · doi:10.1016/s0042-6989(97)00169-7 · Cited by 3,642
Unsupervised texture segmentation using Gabor filters
Jain, A. K., & Farrokhnia, F. (1991) · Pattern Recognition · doi:10.1016/0031-3203(91)90143-s · Cited by 2,182
Unsupervised spike detection and sorting with wavelets and superparamagnetic clustering
Quiroga, R. Q., Nadasdy, Z., & Ben-Shaul, Y. (2004) · Neural Computation · doi:10.1162/089976604774201631 · Cited by 2,119
A dendrochronology program library in R (dplR)
Bunn, A. G. (2008) · Dendrochronologia · doi:10.1016/j.dendro.2008.01.002 · Cited by 2,073
Metadata
- Authors
- Mallat, S. G.
- Venue
- IEEE Transactions on Pattern Analysis and Machine Intelligence
- Published
- 1989-07
- Volume
- 11
- Issue
- 7
- Pages
- 674-693
- ISSN
- 0162-8828 (ISSN-L)
- OpenAlex
- W2132984323
- Cited by
- 21,372
- References
- 3
- FWCI
- 184.71
- Type
- journal article
- Language
- en
- Open access
- closed
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- Mallat, S. G. (1989). A theory for multiresolution signal decomposition: the wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence. https://doi.org/10.1109/34.192463
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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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