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What are the methods to minimize the effect of boundaries in a wavelet decomposition?

I use R and the package waveslim.

I have found for instance the function

?brick.wall

but

  1. I am not too use how to use it.

  2. I am not sure the best solution is to remove some coefficient. I have read somewhere that it exists some wavelets that are not the same everywhere and their shape change at the boudaries.

Any ideas?

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RockScience
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  • Does nobody knows or is the question not interesting? I think the problem arises each time you want to use the wavelet tool for online analysis. Does nobody do online wavelet analysis? – RockScience Mar 07 '11 at 06:03
  • I lost my question acceptation :) you could have written another question don't you ? I'm really busy at the moment but find it still very interesting to dig into your question... might contact you later. – robin girard Apr 24 '13 at 15:20
  • aha sorry for this indeed! But given the enthusiasm of the community for this question, you may end up getting it back again, with a 200 bounty, even without changing your answer ;) – RockScience Apr 26 '13 at 09:27

1 Answers1

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I think this is a good question and I don't kown much about implementations. Since wavelet is 'mutli-resolution' you have two types of solutions (which are somehow connected):

  1. Modify your signal for example extend you signal over the actual boundary to have meaningfull coefficients. Exemples of that are :

    • periodic wavelet on the interval
    • Zero padding (extend the signal by zero outside ist domain
    • finer prodecure are extensions of zero padding with smoothness condition at the boundary.

  2. Modify the wavelet (somehow equivalent to threshold or lower wavelet coefficient that are near the boundary). More generally, there are procedures I know there have been many work since that of A Cohen I Daubechies et P Vial 1993. For example, in (Monasse and Perrier, 1995), wavelet that forms a basis adapted to conditions such as Dirichlet or Neumann are constructed. I guess some are implemented ? If you found implementations, I am interested.

References:

Monasse and Perrier : 1995 CRAS Ondelettes sur lintervalle pour la prise en compte de conditions aux limites

A Cohen I Daubechies et P Vial Wavelets on the interval and fast wavelet transforms Appl Comp Harmonic Analysis (1993)

robin girard
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  • I took some time to look in detail at some of your suggestions. I am working on 2 projects: one to extend the signal in a better way than "periodic" or "reflexion", the other one is the R function ?waveslim::brick.wall, which is a type of wavelet shrinkage applied for boundary issues. Your post is very clear and informative, it deserves my accceptation, thanks! – RockScience May 16 '13 at 05:14