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   -> Volume 2, Issue 5

Question: Implementing C. Chui's semi-orthogonal wavelets.
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Patrick Marais

PostPosted: Fri Nov 29, 2002 2:28 pm    
Subject: Question: Implementing C. Chui's semi-orthogonal wavelets.
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Question: Implementing C. Chui's semi-orthogonal wavelets.


I am currently implementing C. Chui's semi-orthogonal wavelet
decomposition (of images) as part of my master's thesis. I was able to
implement the quadratic scheme without any real problems. However, when
I included code to perform the cubic decomposition, the reconstructed
images were overlayed with a regular grid of lines in some circumstances
as outlined below.

When the number of terms in the detail decomposition sequence,
conventionally named {b}, is increased to about 25, these lines are no
longer evident. At first, I believed my boundary conditions to be at
fault; subsequently, I tried substituting an alternative sequence for
the detail sequence - just the original sequence {b} negated - without
altering my boundary conditions. Obviously, the image was distorted (as
I had expected), however, these lines are no longer visible.

It is possible that my boundary conditions may indeed be in error.
Could some kind soul out there inform me of the methods generally used
to deal with such boundary problems? I have used a periodic
symmetrization to extend the image (fairly standard as far as I know).
Furthermore, I generally only consider image (basis) coefficients
supported on a lattice marginally larger than the original image - this
certainly proved sufficient in the quadratic case. (I have, however,
tried extending this support dramatically for the cubic case, to no
avail). Is there anything else I might consider?

Any help would be greatly appreciated!
Thanks in advance,
Patrick C. Marais

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