Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library: wavelet
See also: dwt invdwt stein hardthres softthres sure

Quantlet: sure2d
Description: Sure denoises wavelet coefficients. If the stein procedure is chosen, the mean squared error is minimized. MSE is estimated by Stein's unbiased risk estimator based on the variance of the coefficients. Sure computes then the optimal threshold for the father wavelets and each level of mother wavelets. If soft or hard thresholding is chosen, only the mother wavelet coefficients will be denoised.

Link:
Usage: datt = sure2d (dat,l,pro)
Input:
dat n x n array, wavelet coefficients
l integer, l^2 is the number of the father wavelet coefficients
pro string, "stein","soft" or "hard" indicating the chosen wished method
Output:
datt n x n array, thresholded wavelet coefficients

Example:

; loads the library wavelet

library ("wavelet")

n = 32

x = grid(0|0, (1./n)|(1./n), n|n ) 

; computes a noisy step function 

y = 0.1*(x[,1].<=0.4) + 2*(abs(x[,1]-0.5).<0.1)

y = y + 0.5*(abs(x[,1]- 0.7)<0.1) 

y = y + 2* x[,2]^2

y = y + normal(n^2) *0.5

y = reshape(y,n|n)

; computes the wavelet coefficients 

coeff  = fwt2 (y, 2, daubechies2,10) 

; thresholds the coefficients 

coefft = sure2d (coeff, 2,"stein") 

; computes the inverse wavelet transform 

ys = invfwt2 (coefft, 2, daubechies2,10) 

d = createdisplay(1,1)

tdat = x~vec(ys)

setmaskp(tdat, 4, 4, 8)

show(d,1,1, tdat, x~vec(y))

Result:

ys denoised estimate of y


Library: wavelet
See also: dwt invdwt stein hardthres softthres sure

Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Author: Yurii Golubev, Stefan Sperlich 980203
(C) MD*TECH Method and Data Technologies, 21.9.2000