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If you want to go even further, Imagemagick can operate on the discrete Fourier transform of an image. The effects are unintuitive but powerful. Read the documentation at:

https://legacy.imagemagick.org/Usage/fourier/#ft_application...

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That's quite interesting. I wonder if it could be used for the blur step because it did take a long while to run.

Noise shows up as light gray lines or dots in the DFT. In the Imagemagick example, this noise is removed by replacing those parts with black. But you want to do the reverse, so you should add noise by adding light gray features to the DFT.

I suspect this technique is how the Imagemagick author generated the noisy twigs image: https://legacy.imagemagick.org/Usage/fourier/twigs.jpg

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