WaveletBestBasis
WaveletBestBasis[dwd]
computes a best basis representation in the DiscreteWaveletData object dwd.
WaveletBestBasis[dwd,cspec]
computes a best basis representation using the cost specification cspec.
Details and Options

- WaveletBestBasis[dwd] returns a DiscreteWaveletData odwd object where the optimal basis has been computed and will be used by functions such as InverseWaveletTransform, WaveletListPlot, etc.
- Properties of the DiscreteWaveletData odwd can be found using odwd["prop"].
- Properties related to best basis include:
-
"BasisIndex" wavelet indices used for inverse transform "BestBasisBlockView" block grid view of best basis "BestBasisCostValues" cost value for each wavelet coefficient "TreeView" tree view of decomposition with best basis highlighted - WaveletBestBasis[dwd] is equivalent to WaveletBestBasis[dwd,"ShannonEntropy"].
- Possible cspec values include:
-
"ShannonEntropy" Shannon entropy "LogEnergy" log energy {"Norm",p} norm like for
and
for
{"Threshold",δ} number of elements above fn apply fn to each coefficient array to get a cost value - A cost function fn must satisfy fn[{a1,…,am,b1,…,bn}]fn[{a1,…,am}]+fn[{b1,…,bn}] and fn[{0,…}]0.
- The best basis is a complete basis for the wavelet decomposition giving the least total cost.
Examples
open allclose allSee Also
DiscreteWaveletPacketTransform StationaryWaveletPacketTransform DiscreteWaveletData InverseWaveletTransform
Related Guides
Introduced in 2010
(8.0)