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Talking about undecimated DWT let's focus here on SWT algorithm.

SWT is said to be:

  • numerically more stable due to Mallat algorithm. And the inverse operation is capable of returning the original signal which is not the case with CWT
  • SWT is computationally faster than CWT

On the other hand:

  • SWT works on dyadic scale while with CWT you can choose any scale sampling

Are there any other factors supporting the choise of one or another alternative?

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  • $\begingroup$ When difference do you make between "non-orthogonal" and CWT? In "DWT produces orthogonal decomposition", how do you link that to the title "In what cases (bi)orthogonal wavelet" $\endgroup$ – Laurent Duval Feb 24 '17 at 7:02
  • $\begingroup$ sorry, I've mixed two questions here in a confusing manner. I'll separate them $\endgroup$ – Alexander Reshytko Feb 26 '17 at 15:54
  • $\begingroup$ The questions are clearer now. I can answer them later in the week, if nobody else does that $\endgroup$ – Laurent Duval Feb 26 '17 at 17:03
  • 2
    $\begingroup$ @LaurentDuval: and the week has passed… $\endgroup$ – DaBler Aug 16 '17 at 13:24
  • $\begingroup$ I should say that I do not fully understand the exact need, and some of the given assertions, eg "SWT works on dyadic scale", can be debated $\endgroup$ – Laurent Duval Aug 16 '17 at 21:24
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Are there any other factors supporting the choice of one or another alternative?

  • possibility to use almost any wavelet shape (and associated sampling) or signal-matched: in favor of the CWT
  • possible parallelization in cycle-spinning form: in favor of SWT
  • tunable redundancy factor: in favor of the CWT
  • possibility to derive sharp signal/noise estimators for denoising: in favor of SWT
  • geometrical extensions (direction, shear, anisotropy) in higher dimension: in favor of the CWT
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