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Science Forum Index » Compression Forum » wavelet compression
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| Yan Yu |
 Posted: Thu Sep 18, 2003 8:47 pm |
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Dear compression experts,
I have a Q on wavelet coefficient:
I have tried wavelet compression on a radar data set.
The results are good.
From what I read, the advantage of wavelet compression is after wavelet
decomposition, most of the wavelet coefficients will be negligible,
therefore you donot need much bits in compressing the few significant
coefficients. but This is contrary to what i observe:
I checked the wavelet coefficients, most of the coefficients are NOT
really negligible (i.e., something close to 0)...
so I wonder what is the definition of "negligible"? Is it "close to 0",
or it is negligible compared to the original data, i.e., "the ratio of a
coefficient over the average of the original data" is close to 0??
Many thanks,
yan |
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| Thomas Richter |
| Posted: Fri Sep 19, 2003 9:52 am |
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Yan Yu wrote:
Quote: so I wonder what is the definition of "negligible"?
There is no real "definition" of this word, this is all rough language,
no precise mathematical definition. What you can say is that
a) errors in the wavelet high-passes are typically less visible in the
image than errors in the image itself,
b) wavelet high-passes have very typical statistics (long-tailed
symmetrical around zero) that makes them easy to compress.
So long,
Thomas |
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| Yan Yu |
| Posted: Fri Sep 19, 2003 3:59 pm |
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Thanks a lot for the explanation!
Thomas Richter wrote:
Quote: Yan Yu wrote:
so I wonder what is the definition of "negligible"?
There is no real "definition" of this word, this is all rough language,
no precise mathematical definition. What you can say is that
a) errors in the wavelet high-passes are typically less visible in the
image than errors in the image itself,
Just to make sure I interprete it correctly, you mean, the same
magnitude of error in the wavelet high-passes, after invert
transformation, will be less visible in the image compared to the same
amount of error in the image??
thanks,
yan
Quote: b) wavelet high-passes have very typical statistics (long-tailed
symmetrical around zero) that makes them easy to compress.
So long,
Thomas
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| Thomas Richter |
| Posted: Sat Sep 20, 2003 6:08 am |
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Yan Yu wrote:
Quote: a) errors in the wavelet high-passes are typically less visible in the
image than errors in the image itself,
Just to make sure I interprete it correctly, you mean, the same
magnitude of error in the wavelet high-passes, after invert
transformation, will be less visible in the image compared to the same
amount of error in the image??
Yes. Note again that this statement is a very rough one. You can clearly
estimate how much error in the decompressed image an error in the
wavelet coefficients will cause, but that depends again on the
definition of "error". I was trying to give a handwaving argument why
wavelets are "nice". The handwaving is that "for typical images and
typical errors, and the typical observer, the results look nicer". If
you want a precise definition of what an "error" is in image
compression, then I would answer with the definition of PSNR.
Unfortunately, it does not give a good visual interpretation of "error".
Two images with the same PSNR might look as having completely different
quality.
So long,
Thomas |
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