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Entropy-based algorithms for best basis selection
Abstract
Adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals. It permits efficient compression of a variety of signals, such as sound and images. The predefined libraries of modulated waveforms include orthogonal wavelet-packets and localized trigonometric functions, and have reasonably well-controlled time-frequency localization properties. The idea is to build out of the library functions an orthonormal basis relative to which the given signal or collection of signals has the lowest information cost. The method relies heavily on the remarkable orthogonality properties of the new libraries: all expansions in a given library conserve energy and are thus comparable. Several cost functionals are useful; one of the most attractive is Shannon entropy, which has a geometric interpretation in this context.>
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Citations
Cited by
Gilles, J. (2013) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2013.2265222 · Cited by 2,210
Feng, Z., Liang, M., & Chu, F. (2013) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2013.01.017 · Cited by 998
Sparse geometric image representations with bandelets
Le Pennec, E., & Mallat, S. (2005) · IEEE Transactions on Image Processing · doi:10.1109/tip.2005.843753 · Cited by 860
A wavelet-based continuous classification scheme for multifunction myoelectric control
Englehart, K., Hudgin, B., & Parker, P. A. (2001) · IEEE Transactions on Biomedical Engineering · doi:10.1109/10.914793 · Cited by 697
Wedgelets: nearly minimax estimation of edges
Donoho, D. L. (1999) · The Annals of Statistics · doi:10.1214/aos/1018031261 · Cited by 638
Metadata
- Authors
- Coifman, R. R., & Wickerhauser, M. V.
- Venue
- IEEE Transactions on Information Theory
- Published
- 1992-03
- Volume
- 38
- Issue
- 2
- Pages
- 713-718
- ISSN
- 0018-9448 (ISSN-L)
- 1557-9654
- OpenAlex
- W2156447271
- Cited by
- 3,188
- References
- 0
- FWCI
- 53.91
- Type
- journal article
- Language
- en
- Open access
- closed
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