Asked by UJJWAL
on 19 Dec 2011

Hi, Suppose I want to add white gaussian noise to an image. I propose to do by following means :- a) imnoise(I,'gaussian',0,0.25); b) I = awgn(I,var(I(:))/0.25); c) I = I + 0.25*randn(size(I));

Here I is a certain image. What is difference between using the above statements ??

Answer by Wayne King
on 19 Dec 2011

Accepted answer

J = imnoise(I,'gaussian',0,0.25); J = I+0.5*randn(size(I));

For awgn(), your function syntax assumes the power of the input is 0 dBW, so you would need to do.

denom = -(var(I(:))/(10*log10(0.25))); I = awgn(I,var(I(:))/denom);

Answer by Wayne King
on 19 Dec 2011

Hi, in

I = I +0.25*randn(size(t));

you get noise with a standard deviation of 0.25, not variance. If you want noise with a variance of 0.25, then you must do

I = I +0.5*randn(size(t));

that would be equivalent to:

imnoise(I,'gaussian',0,0.25);

The variance of a constant times a random variable is the constant squared times the variance of the random variable.

Finally, the actual variance of the additive Gaussian noise in:

I = awgn(I,var(I(:))/0.25);

depends on I, so it's not clear that you are really getting a variance of 0.25. For example:

I = randn(256,256);

Because var(I(:)) = 1.0551 (in this particular example)

Your call of

I = awgn(I,var(I(:))/0.25);

results in an additive WGN process with variance:

10^(-4.2203/10) = 0.3784

which is greater than you think.

Answer by UJJWAL
on 19 Dec 2011

Ok . So suppose the problem is to add a noise with a variance of 0.25 and mean of 0 and the noise is gaussian and additive.

What are the equivalent statements using imnoise, awgn and the first one to introduce such a noise ??

Answer by Shaveta Arora
on 24 Feb 2016

How to add gaussian noise of variance 10 by both methods?

Image Analyst
on 24 Feb 2016

Hint from the help:

Create a vector of 1000 random values drawn from a normal distribution with a mean of 500 and a standard deviation of 5.

a = 5; b = 500; y = a.*randn(1000,1) + b;

For you, a would be sqrt(10) and b would be 0, so

[rows, columns] = size(grayImage); noisyArray = sqrt(10)*randn(rows, columns); output = double(grayImage) + noisyArray;

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