# Simulating Noise in Astronomical Images

I want to add realistic noise to a simulated image but I am a little confused about the process. I want to have some Gaussian random noise representing the readout noise and to also add Poisson noise correlated with the signal in the image.

I understand how to add the Gaussian random noise; I draw samples from a Gaussian with fixed width and add the samples onto the pixel values.

I am confused about the Poisson noise though. Is this noise only correlated to the noiseless signal?

i.e I should draw samples from the Poisson distribution with $$k = \mathrm{pixel value}$$ (before adding the random noise) and add it to the noiseless image.