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I heard of filtering algorithms which, to filter an image specific area, find similar areas in the image and average them to reduce the noice of the original area. E.g. an edge of a house can be more or less the same in the whole image, so one can make many patches from that area and average them. It should be similar to using multiple shots of the same scene and averaging them to make a final image.

What's this algorithm called? I'd like to learn more about it as I found it pretty interesting. But couldn't find them on the Internet so far except some general averaging algorithms.

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Those kind of algorithms are called Non Local algorithms.
The most known algorithms of this family is the - Non Local Means which is a decent Noise Reduction (Denoising) algorithm.

Until the Deep Learning boom, this approach has been extended and usually means working in the Patch Space of image - Patch Based Models and Algorithms for Image Denoising: A Comparative Review Between Patch Based Images Denoising Methods for Additive Noise Reduction.

All those are based on a model in patch based - Average by some kind of a metric / Similarity or some kind of Low Rank model

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