# Determine Gaussian distribution parameters from the signal-to-noise ratio

Is there a straightforward formula for determining the mean and standard deviation of the gaussian distribution followed by noise applied on an image, knowing the signal-to-noise ratio between the original image and the noisy one?

• If you know the signal power, you can know the noise power from SNR, which is the variance of the noise, and the means is usually assumed zero. – BlackMath Oct 8 at 2:45
• Does the expression $SNR = \frac{\mu}{\sigma}$ hold in an image processing context (I found it on wikipedia)? This would boil down to calculating $\sigma = \frac{\mu}{100}$ if the SNR = 20 dB – Hakim Oct 8 at 8:09
• If you mean by $\mu$ signal power. – BlackMath Oct 8 at 15:28
• In my case, it's just the intensities of the pixels. – Hakim Oct 8 at 16:10