Re: (statistics)how to make date more like Laplacian distribution?

"walala" <[EMAIL PROTECTED]> writes:

> Why people think I want to lie upon seeing my question? Oh, it's my problem
> that I did not clearly present the background...

Partly.  Partly also you posed the question in a slightly troll-like
way. :-)

> Here is the story: in deblocking of block DCT coded JPEG images, it was
> known that the DCTed coefficients are Laplacian distributed... But now I am
> looking at low bit rate JPEG images, so there are someking of artifacts...
> in order to reconstruct the original images... many algorithms have been
> devised... one possibility is to make the image coefficients more Laplcian
> like...

These dudes appear to use the fact that the coefficients are Laplacian
to a reasonable level of accuracy:

http://bmrc.berkeley.edu/research/publications/1996/110/imdsp.ps
http://citeseer.nj.nec.com/smoot96study.html

So what makes you say your coefficients are not?  Are you looking at
the right coefficients?

> So that came my question: how to make data more Laplican like...Please give
> me some detailed explanation as I am not veteran in statistics...

Well, what variations do you have available?  Does your modification
have to fit into JPEG? Or can it be seen as a completely separate
step?

Usually, if you want to convert a random variable with one
distribution to another distribution you need to find a function that
relates the two random variables.  

A first, naive, approach might be to use the histogram of the data you
have to find a piece-wise linear function that rescales the data so
that its histogram is Laplacian.

This technique is sometimes used in image processing to make greyscale
images have a uniform brightness distribution (see e.g. 

http://www.cs.tcd.ie/Fergal.Shevlin/courses/4d4/4BA10/PixelBrightnessTransformations.pdf

)

Ciao,

Peter K.

-- 
Peter J. Kootsookos

"I will ignore all ideas for new works [..], the invention of which
 has reached its limits and for whose improvement I see no further
 hope."

- Julius Frontinus, c. AD 84