Wavelet packet transforms and best basis algorithms

Mallet, Y., Coomans, D., and de Vel, O. (2000) Wavelet packet transforms and best basis algorithms. In: Walczak, Beata, (ed.) Wavelets in Chemistry. Data Handling in Science and Technology (22). Elsevier, Amsterdam, The Netherlands, pp. 151-164.

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The wavelet packet transform (WPT) [1] is an extension of the discrete wavelet transform (DWT). The basic difference between the wavelet packet transform and the wavelet transform relates to which coefficients are passed through the low-pass and high-pass filters. With the wavelet transform, the scaling coefficients are filtered through each of these filters. With the WPT, not only do the scaling coefficients pass through the low-pass and high-pass filters, but so do the wavelet coefficients. Since both the scaling and wavelet coefficients are filtered there is a surplus of information stored in the WPT which has a binary tree structure. An advantage of this redundant information is that it provides greater freedom in choosing an orthogonal basis. The best basis algorithm [2] seeks a basis in the WPT which optimizes some criterion function. Thus, the best basis algorithm is a task specific algorithm in that the particular basis is dependent upon the role for which it will be used.

Item ID: 39876
Item Type: Book Chapter (Research - B1)
ISBN: 978-0-444-50111-0
Date Deposited: 17 Aug 2015 23:32
FoR Codes: 01 MATHEMATICAL SCIENCES > 0104 Statistics > 010401 Applied Statistics @ 100%
SEO Codes: 96 ENVIRONMENT > 9699 Other Environment > 969999 Environment not elsewhere classified @ 100%
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