Noise is not only a problem for getting good analytical results in the laboratory, but is an issue for the photographer. In my previous three blogs I presented a theoretical basis for dealing with analytical noise that applies to any measurement process including photography. For the photographer, digital noise is most bothersome in the shadow details. This is because there is less digital information in the shadows than the mid-tones and highlights. Less light means fewer photons, fewer photons mean fewer pixels, and fewer pixels is less digital information. Increasing the sensitivity to boost the signal for low light does not solve the problem, it just increases the noise.
[If you missed the earlier blogs that covered basic theory, don't panic. You can still read them starting with What is Detection and What Does it Mean for Photography. ]
An Approach from the Lab
In earlier blogs I have noted that while an individual measurement near the detection limit has limited value because of the large associated error (i.e., noise is large relative to the measurement), in the context of a data set a collection of measurements has statistical utility even when all of the measurements are near or even below detection. That is because the errors, which are random in nature, average out. The same is true in photography. Consider that each pixel in your image is the consequence of photons striking the sensor. But sometimes the sensor will create more than one pixel for an in-coming photon and sometimes it will create no pixels for in-coming photons. This is a random process, meaning that sometimes the effect will be positive and sometimes negative. If you can average enough random events in a series of nearly identical events, the random noise will be averaged out and canceled.
Consider the following photograph titled It's Really Very Underexposed! The only visible detail is in the sky, where the highlights are. For this shot near sundown, I exposed it so that the highlights in the sky would not be blown and set the f/stop to maximize depth-of-field. (Note a double-click on any of the images will open it at a larger resolution.)
It's Really Very Underexposed!
The problem is that the shadow areas have dramatically less light than the sky and so are totally blocked up (i.e., very few photons). We might conclude that there is nothing of value in the shadows, but to make sure I applied a curves adjustment to get Curves Adjusted to Open Shadows.
Curves Adjusted to Open Shadows
So now it should be obvious that there was light in the shadow areas, but not very much. As a consequence, just like measurements in the lab, when the measurement is near the limit of detection, there is a lot of noise that makes accurate results difficult - but not impossible. See the next image as a crop of the one above to convince yourself that there is a lot of noise in this version (mouse-click the image for a larger more viewable version).
Crop of Curves Adjusted to Open Shadows
So how do you get rid of the noise?