Group: Mathematical Functions
Subgroup: Fourier and Wavelet transforms
See also: invfwt2 fwt invfwt dwt invdwt fwtin fwtinshift
Links:
Wavelet tutorial
Function: fwt2
Description: The algorithm fwt2 is designed for 2 dimensional wavelet transformation. It mainly corresponds to dwt for the one dimensional case. If wished it works with the tensor product of one dimensional wavelet transforms.
Usage: c = fwt2 (x, l, h, a)
Input:
x n x n matrix, the input data, where n has to be a power of 2
l integer, l^2 is the number of the father wavelet coefficients
h m x 1 vector, wavelet basis
a integer, 0,1,2,3,... see notes
Output:
c n x n matrix, resulting coefficients
Notes:
In density or regression estimation the input data have to be realizations on an equispaced grid. The parameter a indicates symmetry properties of 2 dim wavelet transform. The case a = 0 corresponds to the classical 2 dim wavelet transformation. The case a >= log_2(n) gives the tensor product of one dimensional wavelet transforms.
To get the vectors of the wavelet basis, the library wavelet has to be loaded. h can be daubechies2,4,6,8,10,12,14,16,18,20, symmlet4 to 10 or coiflet1 to 5.
Example:
; load the wavelet library 
library ("wavelet") 
; initialize random generator 
randomize(0) 
; generate some data (line from top left to bottom right) 
n = 16 
i = 1:n 
xo = (i.=i') 
x  = xo+0.2.*normal(n,n) 
; compute bivariate wavelet coefficients 
c = fwt2 (x, 4, daubechies4, 0); 
; hard threshold 
c = c.*(abs(c).>0.3) 
; apply inverse transformation 
y = invfwt2(c, 4, daubechies4, 0) 
; compare orginal picture with thresholded picture 
max(max(abs(y-xo),2)I
Result:
Content of object max 
[1,]  0.48421
Group: Mathematical Functions
Subgroup: Fourier and Wavelet transforms
See also: invfwt2 fwt invfwt dwt invdwt fwtin fwtinshift
© XploRe, generated on 6.3.98 7:17 .