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 sum_iTemplateBox[{{w, _, i}}, Abs]^p for and -sum_iTemplateBox[{{w, _, i}}, Abs]^p for
    {"Threshold",δ}number of elements above
    fnapply 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 all

Basic Examples  (1)

Compute an optimal wavelet basis:

In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
Out[2]=

Compare default basis with best basis in a tree plot of all coefficients:

In[3]:=
Click for copyable input
Out[3]=

Scope  (11)

Generalizations & Extensions  (2)

Applications  (3)

Properties & Relations  (4)

Possible Issues  (5)

See Also

DiscreteWaveletPacketTransform  StationaryWaveletPacketTransform  DiscreteWaveletData  InverseWaveletTransform

Introduced in 2010
(8.0)