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I have a little bit confused on the difference between stationary wavelet transform and un-decimated wavelet transform.

So, can anyone tell me, if there is a difference between them?

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  • $\begingroup$ I think both title is the same $\endgroup$ – Zainab Shawqi Dec 25 '15 at 21:14
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The translation invariant version of the DWT is known by a variety of names, including stationary wavelet transform (SWT), redundant wavelet transform, algorithm à trous, quasi-continuous wavelet transform, translation-invariant wavelet transform, shift invariant wavelet transform, cycle spinning, maximal overlap wavelet transform and undecimated wavelet transform.

Ebadi, Ladan, and Helmi ZM Shafri. "A stable and accurate wavelet-based method for noise reduction from hyperspectral vegetation spectrum." Earth Science Informatics (2014): 1-15.

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From what I understand un-decimated wavelet transform (UDWT) involves the elimination of the decimation step to enable DWT to have translational invariance property. The stationary wavelet transform is one such algorithm which is also known as algorithme à trous. There are a number of other algorithms of UDWT a quick google scholar search can you show that but they all use similar ideas to the stationary wavelet transform.

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  • $\begingroup$ But as I think both keep the same length of the signal, i.e. the length of both the high and low pass filter output have the same length like the input signal and from your answer I understand that the difference is only the algorithm, is that correct? $\endgroup$ – Serwan Bamerni Dec 22 '15 at 10:28
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swt is udwt but the signal length in swt must be a power of two for more information check pages 81-87 "Wavelets and their Applications" written by Misiti

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