›

Definition of Wavelet

Alan Karty
in PixInsight
Adam,

What is a wavelet?  You first mention it in the video entitled Elliptical Gradient under Pixel Math, but I don't know what it means.

Thank you.

Alan

Comments

  • BlockHeadBlockHead
    Alan,

    That is a tough one. The explanation requires an understanding of Fourier Transforms. The best I can do is say that it is a mathematical kernal that interacts with data on different scales and frequencies of information. That last part is the thing that requires a bit more information. One consequence of using this mathematical way of interacting with data- is that you can decompose the information into independent scales/frequencies and interact with them. 

    So all of the tools in PixInsight that utilize wavelets have a selection of the number of layers/scales to work with. It is a functionality that is unique to PI in amateur image processing as far as I know. MLT and MMT are examples.

    See what Juan says here:

    (The official forum is always a good place to look for answers.)

    -the Blockhead


  • Ladd Lindsay
    I've been struggling to understand this concept too and was thinking that at some point, I would magically comprehend it.  Lacking that, I've just been "trying" values to see what it does in various projects.  None of the explanations I've seen have really made it clear.  Sine/Cosine functions... I should have paid more attention back in school, but then there is a big difference between theory and practical application.

    As a fundamental concept, a short practical "demonstration" of what it is and how it impacts image processing would be incredibly helpful.  I would add that to my wish list of future videos.  Much like how the excellent drizzle video (recently released) addressed a complicated subject, something similar for wavelets would be incredible!
  • BlockHeadBlockHead
    I did actually try to explain it for a talk I gave at Borrego Springs some years ago. 
    However... I can't say I did it well (or correctly for that matter). 

    One concept I am sure you have heard of is that you can approximate any single valued function (curve) with a superposition of sines and cosines. In electrical engineering the classic is a set of sines/cosines that add up to create square waves. 

    However, this idea (Fourier Transforms) of analyzing images doesn't work well there there are small details (edges). 

    Wavelets are like little snippets of these ideas- so it has both a frequency and spatial component. The spatial component takes care of details and edges. 

    This is a pretty good starter... just listen to the first video...



    -the Blockhead

  • Ladd Lindsay
    That was a good theory explanation.  It makes a little more sense but I still don't understand the practical application related to my images.  For the time being, I'll stick with trial and error.  Having watched how you use it in the lessons has helped nudge me in the right direction.  Sorry Alan, I didn't mean to hijack your topic.  :)
Sign In or Register to comment.