wavelet - Undecimated DWT vs. CWT. In what cases is one preferable over another?

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?

Answer

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