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I have the following image which contains noisy mountains.
In the lower part of the image, the signal-to-noise ratio is too low to contain actual details, but when I remove all the noise from this area, it does not look natural (from my point of view). Why does the noise make an illusion of detail in this case? When should I stop in noise reduction to keep the natural appearance?
Final (slighly removed noise and sharpened):
Original
Original Sharpened
Original Denoised
While there may be truth to the principle that noise adds the illusion of detail, in this example I think you are misinterpreting what you are looking at.
If I remove all the noise in its lower part, it will not look natural (from my point of view)
This is mostly because no noise-reduction algorithm can perfectly remove all noise and retain all detail. The version you get after you run your noise-removal is not an accurate representation of the scene without any noise, but instead is an image that has been altered, removing some noise but along with it removing or altering detail as well.
Different algorithms vary in the final result, but nothing that removes a substantial amount of noise will give you something looking just as "natural" as the original had it not had noise. The variance between algorithms only alters how unnatural, and in what way it is unnatural.
A more appropriate experiment might be to start with an accurate, low-noise photograph and add noise to it.
As to the original claim, noise can at least mask some noticeable artifacts, and masking noticeable artifacts can give the illusion that you started off with a more faithfully accurate image in the first place. Noise can mask banding that you'd otherwise get from 24 bit colour in some gradients, it can mask blocking if the image used lossy compression, and it can mask unnatural smoothing/noise reduction (as in, if an image looks unnatural because of too much noise reduction, adding back in a little bit of noise can mask that and make it look "less unnatural"). That said, in none of these cases is it actually adding any accurate detail, it's just giving the illusion of a more faithful image because it's masking tell-tale signs of unfaithfulness.
Noise is random, it causes gray values to fluctuate from one pixel to the next. This is then random information present at the smallest scale in the picture. If you remove it, then it gives the illusion of the image having become less sharp, as the gray values are not changing as fast on the smallest scale anymore. This doesn't mean that removing the noise is bad per se. Applying aggressive noise reduction can remove real details, but even if you remove the noise using image stacking which actually enhances the real details while removing noise, you will get an image that superficially looks less sharp. But because in this case unsharpness can also be due to misalignment, I'll usually study the image closely to see if there are signs of real problems (sharp edges or pointlike objects will then be more smeared out, or you see ghosting effects there).
This is also affected by the way our perception works. When looking at an image we don't always scan the entire image and reconstruct it in our brains, if we've seen a similar image before we'll just use the old stored version in our brain and just modify it where necessary. The brain tries to interpret what it sees in terms of what it has seen before, in this case it recognizes the new image as an unsharp version of the previous image. This means that people who only see the image with the noise suppressed won't notice the apparent unsharpness.
Noise is not all that random. Most photosite receives photon hits during the exposure. These hits induce an electrical charge. Because the exposing light plays on the sensor for a brief time and because the projected image from the lens is feeble, amplification is needed to strengthen the charge. After the exposure, each photosite charge is sent to a converter and amplifier. The result will assign a digital valve for each site. The amount of amplification is based on the ISO setting and the processing software logic.
It would be ideal if all the amps operated at the same efficiency. However this has yet to be achieved. Each amplifier is an entity with slightly different temperament. The result is an induced static we call noise. This is fixed pattern noise. It shows up as a pattern of pixels that should reproduce with no exposure i.e. black, showing up as dark gray. This is the noise you are taking about.
Add to this blooming. This is what happens when a photosite is oversaturated by too much exposure. Some of the charge leaks out to adjacent photosites. This act induces false data in these adjacent photosites.
In addition to what other participants have said: the algorithm which you used is influencing coarse detail, it is not removing just the fine noise.
I have uploaded the 10px-Gaussian-blurred copies of "original" and "denoised" here:
http://filebin.net/97jdl8sd5t or here https://i.stack.imgur.com/Hrvii.jpg
(you may do it yourself). If you switch between them quickly you will see substantial difference - which is even stronger if images are not blurred.
The answer is: it is not illusion, the shades of "original" image do certainly contain more contrast.
Note 1: there is visible sharpness increase in highlights in "denoised" compared to "original". I do not know about what may have caused it. Note 2: some denoising tools have separate settings for coarse noise (NoiseNinja being an example). Note 3: there is a setting in some denoise tools called "gamma". This setting may affect the aggression of denoising in shadows. "Gamma" is normally set to the gamma of the colour space of the image.
