and 
.Noise
Unwanted signal, such as salt and pepper noise, white gaussian noise, quantization noise.
Probability
Given a random variable x, its
Probability Distribution Function (PDF) is p(x) with
properties and .
We can think of p(x) as being the density of the values between x and x+
Δx. That is, the probability of finding a value between x and x+Δx is p(x)Δx.
Quantization Noise
Suppose that input image is 
, output is 
as in
Consider the difference between g and f to be
quantization noise, 
. For
a simple quantizer, 
. In
this case, quantization noise is uniform [0, 1) with pdf
Mean 
Variance 
Standard deviation 
Poisson Noise
Arises when photons are emitted independently
and randomly, as in radioactive decay or very low light levels. If
emission rate is m photons per unit time T, then the
probability of observing exactly n photons is 
Derived this as limiting case by dividing time T into N bins, such that either 0 or 1 photon is emitted in each bin.
Mean 
Also, variance 
and
standard deviation 
so
signal-to-noise ratio (SNR)
so the SNR goes up at higher emission / count rates.