Different results with approximation coefficients with ndwt and swt
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Should one expect that the results generated from swt and ndwt to match?
I am attempting the following but as one can see, the results are different. Is there anyway to obtain similar denoising characteristics using ndwt as one can obtain with swt?
load noissin;
x = noissin(1:512);
W = ndwt(x,4,'db4','mode','per');
a = indwt(W, 'a', 4);
[swa,swd] = swt(x,4,'db4');
mzero = zeros(size(swd));
b = iswt(swa,mzero,'db4');
subplot(211),plot(a);
subplot(212),plot(b);
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Accepted Answer
Wayne King
on 26 Sep 2013
Edited: Wayne King
on 27 Sep 2013
Dave, what you can do is symmetrically extend the time series, then operate on those wavelet coefficients and then keep the "central" part.
For example:
load Data_GlobalIdx1;
dat = cumsum(diff(log(Dataset.SP)));
N = length(dat);
L = nextpow2(N);
ext = 2^L;
difflen = 2^L-N;
ext = round(difflen/2);
SIG = wextend('ar','sym',dat,ext);
Now I'm going to do something a bit complicated here but, I'm just going to denoise dat before I invert it. This is just the level-dependent universal threshold (with soft thresholding). I'll invert at the end and keep the "central" part and plot the result.
wname = 'db4';
level = 5;
sorh = 's'; % Specified soft or hard thresholding
thrSettings = {...
[...
1 4096 0.387; ...
]; ...
[...
1 4096 0.478; ...
]; ...
[...
1 4096 0.647; ...
]; ...
[...
1 4096 0.966; ...
]; ...
[...
1 4096 1.41; ...
]; ...
};
% Decompose using SWT.
wDEC = swt(SIG,level,wname);
% Denoise.
%---------
len = length(SIG);
for k = 1:level
thr_par = thrSettings{k};
if ~isempty(thr_par)
NB_int = size(thr_par,1);
x = [thr_par(:,1) ; thr_par(NB_int,2)];
x = round(x);
x(x<1) = 1;
x(x>len) = len;
thr = thr_par(:,3);
for j = 1:NB_int
if j==1 , d_beg = 0; else d_beg = 1; end
j_beg = x(j)+d_beg;
j_end = x(j+1);
j_ind = (j_beg:j_end);
wDEC(k,j_ind) = wthresh(wDEC(k,j_ind),sorh,thr(j));
end
end
end
% Reconstruct the denoise signal using ISWT.
%-------------------------------------------
sigDEN = iswt(wDEC,wname);
% now discard the extension
sigDEN = sigDEN(ext+1:ext+length(dat));
plot(dat,'r');
hold on;
plot(sigDEN,'linewidth',2);
legend('Original Data','Denoised Signal');
More Answers (1)
Wayne King
on 25 Sep 2013
Hi Dave, there is a bug in ndwt.m. This has been reported. swt() is correct. Are you not able to use swt() due to length constraints?
The bug in ndwt.m is that the subband filtering only works correctly for the first stage and not subsequently. You can see the results of this bug in the fact that your 'a' vector above has high frequency oscillations when in fact, the approximation coefficients at that level, level 4, should be very smooth (containing no high frequencies)
3 Comments
Wayne King
on 26 Sep 2013
Edited: Wayne King
on 26 Sep 2013
The thing to do here Dave is extend your data vector to a length compatible with the swt() and then truncate it upon output. You have to be a little smart about the way you extend it. Do you have a sample data file you can provide? If you do that and tell me the level of the multiresolution analysis you want and the wavelet you want to use, I can show you an example of how to do that.
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