Creating a noise model with a fixed PSNR
From wikipedia:

$$
    PSNR = 20 \cdot \log_{10}(MAX_I) - 10 \cdot \log_{10}(MSE)
$$

So, you could:


To identify the max value of your image: $MAX_I$
Generate noise samples for $\sigma = 1$
Solve for $MSE$ in the equation above.
Scale all you generated noise samples by the same factor to achieve that $MSE$ value.