Convolution / Wavelets

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Convolution / Wavelets

Post 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


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Re: Convolution / Wavelets

Post by marktownley »

Any software in particular?


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Re: Convolution / Wavelets

Post 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.
Last edited by Alto on Thu Jun 09, 2022 8:03 am, edited 1 time in total.


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Re: Convolution / Wavelets

Post by Montana »

I would guess Filip (Greatattractor) would be the best person to ask about this. Hopefully he might see this post :)

Alexandra


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Re: Convolution / Wavelets

Post 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.


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Re: Convolution / Wavelets

Post 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....


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Re: Convolution / Wavelets

Post 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....


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Re: Convolution / Wavelets

Post 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.)


My software:
Stackistry — an open-source cross-platform image stacker
ImPPG — stack post-processing and animation alignment
My images

SW Mak-Cass 127, ATM Hα scopes (90 mm, 200 mm), Lunt LS50THa, ATM SSM, ATM Newt 300/1500 mm, PGR Chameleon 3 mono (ICX445)
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Re: Convolution / Wavelets

Post by Alto »

With many thanks for your kind patience and assistance. With a plus for the software :bow


Call me Geoff.

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