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I have gone to wavelets course and up to my knowledge, changing the scale and translation of wavelets produces multiresolution images.

is this correct or can someone tell me what is multiresolution analysis in images?

Does multiresolution directly describe wavelet or multiresolution can be achieved other than wavelets?

Emerson EJ
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  • Yes, changing the scale of a wavelet produces different resolutions of the processed image. In practice, you divide the input image into high and low frequency parts, reduce the size (in line with Nyquist sampling theorem), you take the low frequencies and again divide it into high and low frequency parts, recude the size again etc. See https://www.youtube.com/watch?v=DGUuJweHamQ – smcs Nov 14 '18 at 10:09
  • I recommend you the book Multiresolution Signal Decomposition_A.Akansu to get the answers you want. – Fat32 Nov 14 '18 at 10:32
  • @speedymcs So dividing the image into LF and HF components (i.e. approximation and details) and then again splitting LF component into LF and HF until reaching the last scale is multiresolution analysis right? but my doubt is whether this multiresolution analysis is possible only through discrete wavelet transform (DWT) or both DWT & CWT? – Emerson EJ Nov 14 '18 at 11:11
  • I'm still learning it myself but I don't think there is a practical way to compute a CWT. "This multiresolution analysis", as I understand it, is basically the definition of a DWT, so it's not really possible to do it and not call it DWT. – smcs Nov 14 '18 at 11:29
  • There are many fast ways to compute CWT, that differ from DWT, see Should I ever pick the continuous wavelet transform over the discrete one? DWT vs CWT vs STFT – Laurent Duval Dec 30 '18 at 22:05

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The concept of multiresolution has roots on the observation that in data (eg images), objects and features can be observed and processed at different resolutions. One of the crudest version is to build a pyramid with the original image, and other sub-sampled versions, keeping 1 out of 4, 1 out of 16... pixels. This yields a crude multiresolution pyramid, which is not a wavelet per se.

Wavelets, in a strict sense, naturally yield a certain type of multiresolution, but satisfy other constraints (esp. invertibility), so they are only a quite useful way of doing multiresolution.

There are many fast ways to compute CWT, that differ from DWT, see for instance

Laurent Duval
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