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Science Forum Index » Image Processing Forum » Choosing an appropriate wavelet basis...
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 Posted: Wed May 21, 2008 5:59 am |
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Guest
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I have been spending some time learning about and implementing
wavelets, but there is still one lingering question that I have:
How do you go about choosing the best wavelet basis given a priori
knowledge of the exact signal you are applying it to?
In my particular case, I have what looks like a single Gaussian
enveloped sinusoid of a particular bandwidth and center frequency.
This "pulse" is then replicated, shifted, and placed next to the
original pulse to yield a two dimensional image looking something like
this ( a sinusoid in the vertical dimension and shifted versions of
the same sinusoid in the horizontal dimension):
_ _
_ _ _ _
_ _ _ _ _ _
_ _ _ _
_ _
I would imagine that the best basis for a transformation along the
vertical dimension would be the Gaussian enveloped sinusoid itself,
no? If my wavelet and my signal exactly match at a specific scale,
this would mean that there would be a single coefficient at a single
scale and all else would be zeros, right? How do I go about find the
appropriate high pass and low pass analysis and synthesis filters for
this data? Furthermore, if I wanted to do the compression in 2D,
would it make sense to use a different basis for the horizontal
dimension than I use for the vertical dimension? Is this even
possible?
Thanks for your time,
Mike |
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