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2. To enhance a picture, sometimes I do a combination of noise removal (smoothing) and sharpening. Which one should I do last? You know, because those two steps actually "cancel each other".
For standard photo retouch i first denoise using GMIC> enhance> smooth (anisotropic) taking care to not blur the edges but only smear the noise.
After i sharpen, i don't like at all Gimp unsharpmask,
i use instead Unsharpmask2 (that has a exact equivalent in GMIC>Details>sharpen(unsharp) moving "light sharpen" to 0 or close and using only dark sharpening , that has a more natural looking (and if overdone has a more interesting graphic effect then standard unsharpmask )
If you do the contrary you sharpen and enhance all the noise , then you are forced to use more dramatic setting to smear the noise,
this may create interesting special effects BUT is no good for standard editing
And btw is not true that they just "cancel each other" if carefully used good denoising filters didn't blur, at least they don't blur the edges neither the details but only the noise
Even a no sophisticated filter as gaussian blur may be used to blur just the noise, i do always with 3d renders :
on a large image let say 4800x3600 a gaussian blur of 1 has no any visible blurring effect,
EXCEPT for the typical , very little and sharp dots of white or black noise
... a noise that may fool more "smart " denoise filter because so sharp and contrasted that may be read as "details to preserve"
(it will not fool wavelet denoise, but many of the others that identify "the details to preserve" mostly from the contrast with close by pixels )
So first remove at least the most tiny and sharp noise, then sharpen
and yes , after sharpen are few cases where may be useful denoise once again ,(because as may reveal hidden details sharpening may also reveal noise ) but in most cases is not needed