Noise with a Normal Distribution, Mean = 0 and Variance = 100

Answer 3

In this example, each of the 'received' values will have a mean equal to its corresponding 'true' value, and a variance of 100. As you can see from the diagram below, there is now a large degree of overlap between most of the distributions. As in the case of Standard Normal noise, the typical pixel has no noise, but each true value now has about 60 different possibilities for its received value! The probability of any pixel being close to the mean is much smaller; the set bounded by 1 standard deviation on either side of the mean is {45, 46, ..., 64, 65}. There is no systematic shift toward light or dark of the type observed for a large mean. Instead, as you have seen, the pattern of the image begins to disappear: smoothness, texture and edges are obscured by the increasing randomness of all the pixels.


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