## CS/ECE 545 Class 6

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 xx 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.

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