wiener filter and wavelet

[omidi_sbu]

How can I use a wiener filter with wavelet packet transform to have the minimum distortion?

 

[gdarboux]

you may find the answer in Ten Lecture on Wavelets

 

[rasred2004]

How can I use a wiener filter with wavelet packet transform to have the minimum distortion?

the wiener filter is an option of the wavelet packet transfrom as shown in the code of the wavelet packet transform



function w=wpk2d(x,lp,hp,basis)

%WPK2D 2-D Discrete Wavelet Packet Transform
%
% Y = WPK2D(X,H,G,BASIS) calculates the Wavelet Packet
% Transform of vector X. The second argument H is the
% lowpass filter and the third argument G the highpass filter.
% The BASIS argument specifies the desired subband decomposition.
% It can be obtained using a basis selection algorithm.
%
% Run the script 'BASIS' for help on the basis format and 'FORMAT2D'
% for help on the output format.
%


% Uvi_Wave is free software; you can redistribute it and/or modify it
% under the terms of the GNU General Public License as published by the
% Free Software Foundation; either version 2, or (at your option) any
% later version.
%
% Uvi_Wave is distributed in the hope that it will be useful, but WITHOUT
% ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
% FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
% for more details.
%

if (~basis) % trivial case
w=x;
return
end
basis=basis-1;

wx=wt2d(x,lp,hp,1); % perform one analysis level
% into the analysis tree

if all(basis==0) % four ending nodes achieved
w=wx;
return
end

[ly,lx]=size(wx); % separate approximation and details
a=wx(1:ly/2,1:lx/2); % at the analysis output
v=wx(ly/2+1:ly,1:lx/2);
h=wx(1:ly/2,lx/2+1:lx);
d=wx(ly/2+1:ly,lx/2+1:lx);


% Approximation case

tope=1; % finds the point where the
suma=2^(-basis(1)*2); % basis vector must be divided
i=1; % in order to call the recursion
while (suma<tope)
i=i+1;
suma=suma+2^(-basis(i)*2);
end

if all(basis(1:i)~=0) % a level with an ending node
wa=wpk2d(a,lp,hp,basis(1:i)); % but the other node continues
else wa=a;
end


% Vertical residue case

basis=basis(i+1:length(basis));
suma=2^(-basis(1)*2);
i=1;
while (suma<tope)
i=i+1;
suma=suma+2^(-basis(i)*2);
end

if all(basis(1:i)~=0)
wv=wpk2d(v,lp,hp,basis(1:i));
else wv=v;
end


% Horizontal residue case

basis=basis(i+1:length(basis));
suma=2^(-basis(1)*2);
i=1;
while (suma<tope)
i=i+1;
suma=suma+2^(-basis(i)*2);
end

if all(basis(1:i)~=0)
wh=wpk2d(h,lp,hp,basis(1:i));
else wh=h;
end


% Diagonal residue case

basis=basis(i+1:length(basis));

if all(basis~=0)
wd=wpk2d(d,lp,hp,basis);
else wd=d;
end

% arrangement of the band sizes
% it is necessary when any of the original sizes is not a power of 2

c1=size(wa,2)-size(wv,2); % difference in the number of columns
if c1<0 % between the approx. and vertical residue band
wa=[zeros(size(wa,1),-c1) wa]; % we add blank columns to the smallest,
elseif c1>0 % in order to match band sizes
wv=[zeros(size(wv,1),c1) wv];
end

c2=size(wh,2)-size(wd,2); % idem, between horizontal and diagonal residues
if c2<0
wh=[zeros(size(wh,1),-c2) wh];
elseif c2>0
wd=[zeros(size(wd,1),c2) wd];
end

f1=size(wa,1)-size(wh,1); % difference in the number of rows
if f1<0 % between the approx. and horizontal residue band
wa=[zeros(-f1,size(wa,2)) ; wa]; % we add blank rows to the smallest,
elseif f1>0 % in order to match band sizes
wh=[zeros(f1,size(wh,2)) ; wh];
end

f2=size(wv,1)-size(wd,1); % idem, between vertical and diagonal residues
if f2<0
wv=[zeros(-f2,size(wv,2)) ; wv];
elseif f2>0
wd=[zeros(f2,size(wd,2)) ; wd];
end

w=[ [wa,wh] ; [wv,wd] ]; % fit the four bands

Added after 6 minutes:

How can I use a wiener filter with wavelet packet transform to have the minimum distortion?

if you need any help and you do not know how to use the matlab code just send me a e.mail

rasred2004@yahoo.com