How does averaging images or lowering resolution reduce noise?

This answer lists 3 techniques to reduce noise:

• Keep the camera's sensor cool.


• Take a burst of photos, then average them.


• Lower the resolution.

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?

Answer

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:

• you can let the camera cool between captures, helping with issue #1


• long exposures only work if you capture more light, which means keeping the aperture constant and lowering the ISO value (which is not always possible, e.g. if you hit the minimum ISO value)


• longer exposures can introduce camera shake, which can be avoided using several shorter exposures (though the images will need alignment).

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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.