Do variance get increased by increasing SNR?

I have added SNR of 20 to an image using the below formula of variance

SNR = [var(image)/var(noise)]
var(noise)=var(image)/SNR

in matlab code...

v = var(I(:)) / 10;% SNR=10
I_noisy = imnoise(I, 'gaussian', 0, v);

Is it correct?...

Answer 1

[Image Analyst]

No, it's not. Well maybe it might be close if your image was 100% noise and no signal. Otherwise there is no basis for your assumption that the noise is the same as the variance of the image.