How to eliminate image noise in the form of a fine pattern without clear patterns?

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Increase (400%)
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Zoom (1600%)
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It is desirable that the gradient remained, and the contrast too has not changed. That is, all the same, only solid colors and the gradient (where it exists), and on the borders of regular (not sharp) transition in 1 pixel. On this picture is white, black, brown, and the gradient from blue to orange, plus halftone of 1 pixel at the borders between colors.

Maybe there are already ready decisions - the filters that can, really? If not, what algorithm is better to use to create your own filter? Or combination of algorithms?
April 3rd 20 at 18:38
1 answer
April 3rd 20 at 18:40
In photoshop there is a Smart Blue blur, we need to play that specific pattern better cope. It is only after the blur without changing the sharpness/contrast and other things

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