I enjoy reading this author's articles such as the one explaining auto-differentiation [1]. Before that, I tried to understand this survey on auto-differentiation [2], and it just didn't click for me. The analogy to imaginary numbers was perfect.
Great article. The author also links to Steve Brunton's video on A Compressed Overview of Sparsity. I found Mr. Brunton's channel only recently myself and found it to be a treasure trove of information. Highly reccomended.
There was an article that demonstrated scratch removal by zeroing out (or was it blurring?) the its dual in the DCT domain. Unfortunately I can't dig it up.
Here are a few resources for periodic pattern removal (e.g. in halftone print images) by zeroing out parts of the image in the Fourier domain. Maybe that was what you had in mind?
I did exactly that in a grad level image processing take home final and got a 70. There were other corruptions in the image. The professor never taught anything about image correction or evaluating error, he wanted to see what I came up with. I still don’t understand that grade.
Found it[1]. I misremembered a bit, they demonstrated how to remove periodic noise, then left "remove the string" as an exercise for the reader (bottom of the page).
[1] https://blog.demofox.org/2014/12/30/dual-numbers-automatic-d...
[2] https://arxiv.org/abs/1502.05767v4