Gaussian Noise vs Gaussian White Noise

Question

How Gaussian noise differs from white Gaussian noise? As I read Gaussian noise has PDF of normal distribution. Does the white Gaussian noise have it too?

How can I manually (without built-in functions) generate each of the noise for an image using Python? Which parameters do I need to consider?

Answer 1

Lets examine the phrase White Gaussian Noise starting from the end.

• Noise - This only says about the usage. Has nothing to do with its properties.
• Gaussian - The values are following (Extracted) from Gaussian (Normal) Distribution.
• White - The values are not correlated. Namely you can infer no data from one sample on a different sample (Since in Gaussian Distribution no Correlation -> Independence). Also tells us the Power Spectrum of the Auto Correlation function is Flat (Or the Auto Correlation itself is the Delta Function).

Now, regarding how to generate them.
Basically most Random Number Generators generate Uniform Data which then some transformation is applied on to generate any other wanted distribution (See https://en.wikipedia.org/wiki/Probability_density_function#Dependent_variables_and_change_of_variables for some idea on how it is done).

To create non white data you need to create some linear connection between samples.
Namely, just mix few samples with linear weights.
It is usually done by applying some kind of a filter on the data.