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*+Δ*x*. That is, the
probability of finding a value between *x* and
*x*+Δ*x* 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.

CS/ECE 545 Staff

Contents ©1997 - 2011 Norman Wittels and Michael A. Gennert