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   -> Volume 7, Issue 6


Question: 2D wavelet transforms
 
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Black Adder (blackadr@bigfoot.com)
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PostPosted: Wed May 27, 1998 9:12 pm    
Subject: Question: 2D wavelet transforms
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#21 Question: 2D wavelet transforms

Dear Waveleteers,

This is a very elementary question since I've just started dipping
into wavelets. My interest in wavelets stems from my interest in
image compression and image processing in general. Since I don't have
a very strong mathematical background, some of my questions will seem
pathetic :) Just bear with me.

Question 1:

When I want to compress and image using, say, the Haar wavelet, I
first apply the (1-D averaging and differencing) transformation to
each row and then to each column _of the resulting coarse
coefficients_. First my image gets squished horizontally, leaving a
similar rectangle of detail coefficients to its right. Then the
squished image gets squished vertically (back into proportion) and
leaves a similar rectangle of detail coefficients below it. I dont
apply the (vertical) Haar Transform to the detail coefficients from
the first (horizontal) transformation. Is this the correct way to
perform a 2-D Transform?

Question 2:

I read some of Wim Sweldens' excellent paper "Building Your Own
Wavelets at Home". I must say that I like Wim's way of writing much
better than most other peoples'. In it he mentions interpolating
polynomials which can be used to predict the odd coefficients using
just the even ones. Initially I thought of using Lagrange polynomials
to do the prediction. Then I thought of using cubic (or higher order)
splines to do that. Assuming I have a vector containing 16 elements,I
subsample it to obtain two vectors of length 8 each. Now, can I use a
7th degree spline to predict all the odd coefficients (this reducing
the number of polynomials I have to calculate) or do I have to have
smaller order polynomials?

Thank you for reading and (hopefully) answering my naive questions.

--Shahbaz
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