[norrius]

If you do something really simple like a Gaussian blur (which is a type of convolution), it might be possible to find the inverse convolution (de-convolution) and restore the original image with some accuracy.

One method is the Lucy-Richardson deconvolution [1], which is an iterative algorithm, and here [2] is the best practical example I could find right away. Unfortunately the text is not in English, but the illustrations and formulae might be enough to give some intuition of the process.

[1] https://en.wikipedia.org/wiki/Richardson%E2%80%93Lucy_deconv...

[2] https://habr.com/en/post/136853/

[buzzier]

https://github.com/Y-Vladimir/SmartDeblur

http://smartdeblur.net/

[norrius]

Yes, that's it, thank you! And here's the English version of the article I linked above: https://yuzhikov.com/articles/BlurredImagesRestoration1.htm

[barbegal]

Yes this is possible before JPEG compression, because convolution removes fairly little information but once you compress using JPEG you remove the frequency components that make it reversible.