This answer lists 3 techniques to reduce noise:
Can someone shed more light about the last two techniques?
How can taking many photos and average them reduce the noise? How does one average them? And why does this would work?
How does lowering the resolution reduce noise?
The last two are really the same thing and works due to the fact that in most cases noise is just as likely to push the value of a pixel up as it is to pull the value down.
Let's say the 'true' value of a given pixel is 100 (out of 255). Take 10 images of the same scene in noisy conditions and you might record the following values:
104, 99, 98, 100, 101, 105, 99, 102, 94, 105
averaging these values (by adding them up and dividing by 10) gives the following pixel value: 100.7, which will round to 101, which is much closer to the true value than you would expect to be if you had to choose only one of the 10 images at random.
As for the how, there are specialist software packages for this (search for image stacking, I think Deep Sky Stacker is a popular choice). Alternatively you can do it in most image editing by loading several layers and merging pairs of layers (more recent versions of photoshop have special stacking functions which are a bit better).
The same principal lies behind reducing the resolution. One technique to do this is called 'binning' whereby you combine four adjacent pixels into one. So imagine four pixels corresponding to an area of flat colour within the image, which ought to have a uniform value of 100:
102, 103
93, 101
averaging them gives a single pixel with value of 99.75 which rounds to 100.
Incidentally, taking several images and averaging them is equivalent to taking a longer exposure except:
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Finally, when it comes to minimising noise the golden rule is to get as much light as possible. Averaging several exposures does this (it's total light captured that matters). Downsampling is really trading noise for resolution.
In silicon there is an effect called thermal noise (Johnson noise). This is basically electrons been torn loose from the substrate and adding to the electrons being knocked loose by photons. These electrons are then considered part of the "signal" from the sensor, creating noise. This kind of noise is Gaussian distributed and have a mean value of zero.
Thermal noise increases with temperature, that's why a cooler sensor performs better.
This only works for random noise with an average of zero. If the noise is random (enough) it's never quite the same, while the scene you're taking a picture of should be. Since information about the scene is recorded several times, each time with slightly different noise it's possible to average the pixels and get a higher signal to noise ratio than from one capture. This means that the scene needs to be static.
Depending on how the larger sensor is achieved you might get less noise. One technique is to keep the physical sensor size constant, and then combine several physical pixels into one logical one. Or the physical size of the sensor can be different.
By combining several physical pixels into one logical one you can achieve the same kind of noise reduction as by combining several captures.
By increasing the physical size of the pixel it's possible to reduce noise from readout and amplification. With a larger pixel, it's a larger number of electrons in the signal. Since the readout and amplification noise is close to fixed for any given production technology (transistor size) it's possible to achieve a larger signal to noise ratio.
Here's an article which nicely explains the concept behind averaging and how to do it by hand with Photoshop. The same technique can be used in any image editing software that supports layers and layer opacity.
