Wavelet Packets - MULTIMEDIA

Wavelet packets can be viewed as a generalization of wavelets. They were first introduced by Coifman, Meyer, Quake, and Wickerhauser as a family of orthonormal bases for discrete functions of RN. A complete subband decomposition can be viewed as a decomposition of the input signal, using an analysis tree of depth log N.

In the usual dyadic wavelet decomposition, only the low - pass - filtered subband is recur­sively decomposed and thus can be represented by a logarithmic tree structure. However, a wavelet packet decomposition allows the decomposition to be represented by any pruned subtree of the full tree topology.

Therefore, this representation of the decomposition topol­ogy is isomorphic to all permissible subband topologies. The leaf nodes of each pruned subtree represent one permissible orthonormal basis, The wavelet packet decomposition offers a number of attractive properties, including

  1. Flexibility, since a best wavelet basis in the sense of some cost metric can be found within a large library of permissible bases
  2. Favorable localization of wavelet packets in both frequency and space.
  3. Low computational requirement for wavelet packet decomposition, because each decomposition can be computed in the order of N log N using fast filter banks.

Wavelet packets are currently being applied to solve various practical problems such as image compression, signal de - noising, fingerprint identification, and so on.

Haar wavelet decomposition. Courtesy of Sieve Kilthau

Haar wavelet decomposition. Courtesy of Sieve Kilthau

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