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   -> Volume 4, Issue 11

Question: Fractional Brownian Noise
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"Simon, Stephen (Steve)" (sis1@NIOBBS1.EM.CDC.GOV)

PostPosted: Fri Dec 06, 2002 9:36 am    
Subject: Question: Fractional Brownian Noise
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Question: Fractional Brownian Noise

I have a signal plus noise problem where the noise looks in many ways
like a fractional brownian process. I have lots of data with all
noise and no signal and in these cases, the variability in the wavelet
coefficients appear to follow a power law. I have been tinkering with
a thresholding rule that incorporates this power law. In simple
terms, I zero out the coefficients at the highest "frequency" if they
are within plus/minus K, at the next highest "frequency" if they are
within plus/minus K*2**alpha, at the next "frequency" if they are
within plus/minus K*2**(2*alpha), etc., where alpha is based by the
degree of self-similarity (self-affinity) of the noise. Traditional
thresholding rules preserve as part of the signal certain low
frequency patterns that are an artifact of the correlational nature of
the noise. So far, the power law seems to do a much better job of
separating signal from noise.

Before I go to a lot of trouble on this, is there any reference on the
use of wavelet decomposition on fractional brownian processes? I've
seen a few references on how wavelets "whiten" a process, but I want
to see results on the variability of the wavelet coefficients at each
"frequency" level.

Also, has anyone seen references on the use of a power law for
thresholding wavelet coefficients?

Steve Simon,
Standard disclaimer.

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