Generating random noise in matlab

Question

When I add Gaussian noise to an array shouldnt the histogram be Gaussian? Although the noise is random, the distribution should be gaussian right? That is not what I get.

A=zeros(10);
A=imnoise(A,'gaussian');
imhist(A)

Answer 1

Two things could be going on:

1. You don't have enough of a sample size, or

2. The default mean of imnoise with gaussian distribution is 0, meaning you're only seeing the right half of the bell curve.

Try

imhist(imnoise(zeros(1000), 'gaussian', 0.5));

Answer 2

This is what your code is doing:

A = zeros(10);

mu = 0; sd = 0.1;                 %# mean, std dev
B = A + randn(size(A))*sd + mu;   %# add gaussian noise

B = max(0,min(B,1));              %# make sure that 0 <= B <= 1

imhist(B)                         %# intensities histogram

can you see where the problem is? (Hint: RANDN returns number ~N(0,1), thus the resulting added noise is ~N(mu,sd))

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Perhaps what you are trying to do is:

hist( randn(1000,1) )

Answer 3

imnoise() is a function that can be applied to images, not plain arrays.
Maybe you can look into the randn() function, instead.

Answer 4

You might not see a bell-curve with a sampling frame of only 10.

See the central limit theorem.

http://en.wikipedia.org/wiki/Central_limit_theorem

I would try increasing the sampling frame to something much larger.

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Reference:

Law of Large Numbers

http://en.wikipedia.org/wiki/Law_of_large_numbers