How can you automatically eliminate noise in the form of a small pattern in the image without a clear pattern?

Question

Algorithms

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In this case, it is desirable that the gradient remains, and the contrast also does not change. That is, everything is the same, only solid colors and a gradient (where it is), and on the borders there is a normal (not sharp) transition of 1 pixel. In this picture, it's white, black, brown, and a blue to orange gradient, plus 1 pixel halftones on the borders between the colors.
Maybe there are already ready-made solutions - filters that can do this? If not, what is the best algorithm to apply to create your own filter? Or a combination of algorithms?

Answer 1

There is a Smart Blue blur in Photoshop, you need to play with the parameters to better cope with a specific pattern. This is only after blurring, without changing the sharpness / contrast and other things