Wavelet Toolbox    
wentropy

Entropy (wavelet packet)

Syntax

Description

E = wentropy(X,T,P) returns the entropy E of the vector or matrix input X. In both cases, output E is a real number.

E = wentropy(X,T) is equivalent to E = wentropy(X,T,0).

T is a string containing the type of entropy and P is an optional parameter depending on the value of T.

Entropy Type Name (T)
Parameter (P)
Comments
'shannon'

P is not used
'log energy'

P is not used
'threshold'
0 P
P is the threshold
'sure'
0 P
P is the threshold
'norm'
1 P
P is the power
'user'
string
P is a string containing the M-file name of your own entropy function, with a single input X
FunName
No constraints on P
FunName is any other string except those used for the previous Entropy Type Names listed above.
FunName contains the M-file name of your own entropy function, with X as input and P as additional parameter to your entropy function.

Functionals verifying an additive-type property are well suited for efficient searching of binary-tree structures and the fundamental splitting property of the wavelet packets decomposition. Classical entropy-based criteria match these conditions and describe information-related properties for an accurate representation of a given signal. Entropy is a common concept in many fields, mainly in signal processing. The following example lists different entropy criteria, many others are available and can be easily integrated. In the following expressions, s is the signal and (si)i the coefficients of s in an orthonormal basis.

The entropy E must be an additive cost function such that E(0) = 0 and

Examples

References

Coifman, R.R.; M.V. Wickerhauser (1992), "Entropy-based Algorithms for best basis selection," IEEE Trans. on Inf. Theory, vol. 38, 2, pp. 713-718.

Donoho, D.L.; I.M. Johnstone, "Ideal de-noising in an orthonormal basis chosen from a library of bases," C.R.A.S. Paris, Ser. I, t. 319, pp. 1317-1322.


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