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Convolution / Wavelets

Posted: Mon Jun 06, 2022 4:11 pm
by Alto
Can anyone recommend a source (simple explanation) for what the various convolution and wavelet processes do when they affect our astronomy images.
I found a stacking tutorial that helped my understanding of what's really happening, just need a similar guide to the next stage in the sequence.

Cheers Geoff

Re: Convolution / Wavelets

Posted: Mon Jun 06, 2022 5:29 pm
by marktownley
Any software in particular?

Re: Convolution / Wavelets

Posted: Tue Jun 07, 2022 11:20 am
by Alto
None in particular Mark.

Just interested in what happens at the level of the pixels to understand the underlying mechanics to teach the final images.

I still use imPPG for preference, with recent dabbles in Astrosurface - though that latter one is proving less easy to use at the moment.

Re: Convolution / Wavelets

Posted: Wed Jun 08, 2022 6:56 am
by Montana
I would guess Filip (Greatattractor) would be the best person to ask about this. Hopefully he might see this post :)

Alexandra

Re: Convolution / Wavelets

Posted: Wed Jun 08, 2022 6:17 pm
by GreatAttractor
I can speak to what ImPPG does: non-blind Lucy-Richardson deconvolution with a Gaussian kernel.

It assumes that the original, sharp image (as would be seen by your telescope placed just outside Earth's atmosphere) has been effectively¹ convolved with a Gaussian kernel. As if someone just applied "Gaussian blur" to it. The L-R method tries its best to undo the blur (while also keeping noise in check). If the input stack is of OK-ish quality, what you get is quite close to the original. The sigma (σ) parameter which you can tune in ImPPG is the standard deviation mentioned in the Wikipedia article, i.e., a measure of the kernel's width.



¹ Due to seeing effects and fuzziness inherent in the stacking process.

Re: Convolution / Wavelets

Posted: Thu Jun 09, 2022 6:25 am
by Alto
Thanks GA.

So the process is effectively making an attempt to remove the earth's atmosphere (the blur) from the telescope image?

It's the how that is intriguing....

Re: Convolution / Wavelets

Posted: Thu Jun 09, 2022 8:10 am
by Alto
Not exactly a simplified explanation, nor helped by somewhat 'poor' subtitling!

https://www.youtube.com/watch?v=3G7dss9_fos

Gives me a clue of sorts, especially as it is related to astronomy images....

Re: Convolution / Wavelets

Posted: Thu Jun 09, 2022 6:52 pm
by GreatAttractor
Thanks, that's a very cool video.

As to the "how" of L-R deconvolution in particular, I didn't ponder it too much - just read the Wikipedia article, and implemented the described operations.
It has been shown empirically that if this iteration converges, it converges to the maximum likelihood solution for uⱼ.
(where uⱼ are the pixel values of the undistorted image.)

Re: Convolution / Wavelets

Posted: Fri Jun 10, 2022 7:57 am
by Alto
With many thanks for your kind patience and assistance. With a plus for the software :bow