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For the isotropic wavelet packet transform it is proposed to force a maximum decomposition depth for the approximation subband.

This increase is due to the fact that the anisotropic transform has substantially more WP for a comparable maximum decomposition depth.

D l, g c gives the expected decomposition depth of a subband at level l with a maximum decomposition depth of g.

D l, g a c gives the expected decomposition depth of a subband at level l with a maximum decomposition depth of g.

The probability of a decomposition of a subband depends on the number of sub-transforms within the subband, which is equivalent to Q g-l where g is the maximum decomposition depth and l is the level of the subband.

For the anisotropic wavelet packet transform, in addition to forcing a maximum decomposition depth, the maximum degree of anisotropy for the approximation subband needs to be restricted to preserve compression performance.

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Similar(52)

The number of possible WP is huge even for moderate maximum decomposition depths (e.g., 2261.6 for isotropic g = 5, and 21321.9 for an anisotropic depth of 10).

Since the number of anisotropic WP is by far greater than the number of isotropic WP (for comparable maximum decomposition depths, remember an isotropic decomposition depth g corresponds to an anisotropic decomposition depth of 2 g), the anisotropic case has to be considered secure as well.

The started decomposition temperature and the maximum decomposition temperature are at 323.5 and 396.2 °C, respectively.

Therefore, a decomposition depth of 2 g in the anisotropic case is comparable to a decomposition depth of g in the isotropic case.

Table 5 The expected average decomposition depth for anisotropic WP distributions (b = 1/ 4, c = 0) Aniso.

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