Wikipedia:Reference desk/Archives/Mathematics/2023 July 5

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July 5

2d Discrete Poisson Equation and Gradient Image Processing

The 2d discrete Poisson Equation comes up in the context of gradient domain image processing; recently, I have a need to implement a solver for this problem. While some libraries already exist, I would prefer to code my own. However, the only thing I can find on the topic are journal articles that are very jargon heavy and terse - and that's fine and expected - since this is not my area of expertise, it is rough going and, as such, I was hoping someone might be able to suggest a a book or reference that covers the problem without assuming quite as much background. To be precise, a lot of the jargon seems related to numerical methods and partial differential equations and these are subjects I haven't touched in a while; something that spent more than a few paragraphs before jumping into what they do with the solutions would be helpful. Thank you in advance:-)2601:547:1500:C60:C59B:AA40:33AD:4711 (talk) 16:36, 5 July 2023 (UTC)

Are these lecture notes helpful, or are they also too jargon-laden and terse? They do not explain the fastest solution method, which uses a multigrid method, but FFT is possibly fast enough for you. If you need the speed of multigrid, consult these notes.  --Lambiam 19:29, 5 July 2023 (UTC)

Thank you so much, those are wonderful! The image processing articles I was reading sort of just skipped over how to solve it, that's much clearer and workable.2601:547:1500:C60:C59B:AA40:33AD:4711 (talk) 19:38, 5 July 2023 (UTC)