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The discrete wavelet transform: wedding the a trous and Mallat algorithms
Open accessAbstract
Two separately motivated implementations of the wavelet transform are brought together. It is observed that these algorithms are both special cases of a single filter bank structure, the discrete wavelet transform, the behavior of which is governed by the choice of filters. In fact, the a trous algorithm is more properly viewed as a nonorthonormal multiresolution algorithm for which the discrete wavelet transform is exact. Moreover, it is shown that the commonly used Lagrange a trous filters are in one-to-one correspondence with the convolutional squares of the Daubechies filters for orthonormal wavelets of compact support. A systematic framework for the discrete wavelet transform is provided, and conditions are derived under which it computes the continuous wavelet transform exactly. Suitable filter constraints for finite energy and boundedness of the discrete transform are also derived. Relevant signal processing parameters are examined, and it is observed that orthonormality is balanced by restrictions on resolution.>
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Cites
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
Chen, L.-C., Papandreou, G., Kokkinos, I., Murphy, K., & Yuille, A. L. (2018) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2017.2699184 · Cited by 22,392
Chen, L.-C., Papandreou, G., Kokkinos, I., Murphy, K., & Yuille, A. L. (2016) · arXiv · doi:10.48550/arxiv.1606.00915 · Cited by 22,392
Aiazzi, B., Alparone, L., Baronti, S., & Garzelli, A. (2002) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2002.803623 · Cited by 855
A comparative analysis of image fusion methods
Wang, Z., Ziou, D., Armenakis, C., Li, D., & Li, Q. (2005) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2005.846874 · Cited by 852
Axial-DeepLab: Stand-Alone Axial-Attention for Panoptic Segmentation
Wang, H., Zhu, Y., Green, B., Adam, H., Yuille, A., & Chen, L.-C. (2020) · Lecture Notes in Computer Science · doi:10.1007/978-3-030-58548-8_7 · Cited by 809
Metadata
- Authors
- Shensa, M. J.
- Venue
- IEEE Transactions on Signal Processing
- Published
- 1992
- Volume
- 40
- Issue
- 10
- Pages
- 2464-2482
- ISSN
- 1053-587X (ISSN-L)
- OpenAlex
- W2116988482
- Cited by
- 1,994
- References
- 1
- FWCI
- 30.61
- Type
- journal article
- Language
- en
- Open access
- green
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