# 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

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## Basic Examples(1)

Compute an optimal wavelet basis:

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

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