Methods for quantifying image noise are presented in the next sections in terms of the photographic imaging process, where noise fluctuations are measured in density units (denoted D). The methods can be applied quite generally to other imaging systems where the fluctuations might, for instance, be luminance or digital value.
Although we are dealing with two-dimensional images it is usual to confine noise analysis to one spatial dimension. This simplifies the methods and is entirely adequate for most forms of noise.
We begin by assuming we have a noise waveform D(x) - the variation of output in one direction across a nominally uniform sample of image.
This is the mean square noise, or the total noise power, and is useful for summarizing the amplitude variation of the (Gaussian) random function. It is defined:
where AD(x) is the deviation of D(x) from the mean.
The expression for variance, o2, is replaced by a discrete version for the purpose of calculation:
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