wpdec2 :: Functions (Wavelet Toolbox™)

wpdec2

Purpose

Wavelet packet decomposition 2-D

Syntax

T = wpdec2(X,N,'wname',E,P)
T = wpdec2(X,N,'wname')

Description

wpdec2 is a two-dimensional wavelet packet analysis function.

T = wpdec2(X,N,'wname',E,P) returns a wavelet packet tree T corresponding to the wavelet packet decomposition of the matrix X, at level N, with a particular wavelet ('wname', see wfilters for more information).

T = wpdec2(X,N,'wname') is equivalent to T = wpdec2(X,N,'wname','shannon').

E is a string containing the type of entropy and P is an optional parameter depending on the value of T (see wentropy for more information).

Entropy Type Name (E)
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.

STR
No constraints on P
STR is any other string except those used for the previous Entropy Type Names listed above.
STR contains the M-file name of your own entropy function, with X as input and P as additional parameter to your entropy function.

Entropy Type Name (E)	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`.
`STR`	`No constraints on P`	`STR` is any other string except those used for the previous Entropy Type Names listed above. `STR` contains the M-file name of your own entropy function, with `X` as input and `P` as additional parameter to your entropy function.

Note The 'user' option is historical and still kept for compatibility, but it is obsoleted by the last option described in the preceding table. The FunName option does the same as the 'user' option and in addition, allows you to pass a parameter to your own entropy function.

See wpdec for a more complete description of the wavelet packet decomposition.

Remarks

When X represents an indexed image, X is an m-by-n matrix. When X represents a truecolor image, it is an m-by-n-by-3 array, where each m-by-n matrix represents a red, green, or blue color plane concatenated along the third dimension.

For more information on image formats, see the image and imfinfo reference pages.

Examples

% The current extension mode is zero-padding (see dwtmode).

% Load image. 
load tire 
% X contains the loaded image.

% For an image the decomposition is performed using: 
t = wpdec2(X,2,'db1'); 
% The default entropy is shannon.

% Plot wavelet packet tree 
% (quarternary tree, or tree of order 4). 
plot(t)

Algorithm

The algorithm used for the wavelet packets decomposition follows the same line as the wavelet decomposition process (see dwt2 and wavedec2 for more information).

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.

Meyer, Y. (1993), Les ondelettes. Algorithmes et applications, Colin Ed., Paris, 2nd edition. (English translation: Wavelets: Algorithms and Applications, SIAM).

Wickerhauser, M.V. (1991), "INRIA lectures on wavelet packet algorithms," Proceedings ondelettes et paquets d'ondes, 17-21 June, Rocquencourt, France, pp. 31-99.

Wickerhauser, M.V. (1994), Adapted wavelet analysis from theory to software Algorithms, A.K. Peters.