The model of noise in Image denoising problem
Theory behind it: the additive Gaussian noise  can be related to (Johnson–Nyquist) thermal noise in standard images. For the  denoising of more generic multivariate images, chapter 2.2.2 provides some references on why global noise present in acquired data can be realistically modelled by an additive zero-mean spatially white Gaussian noise. 

The shot noise can be modeled as a Poisson process, that behaves, for large numbers, like a Gaussian noise. 

Other types of noises are observable in images: salt-and-pepper, quantization (more uniform), grain. In some image modalities, noise can be not stationary, multiplicative. They can be modeled by stochastic  processes in general.

Gaussian noise is also widely used because it enjoys relatively tractable theories, related to least-square estimation. A very practical reason.

Note, however, that most images have 8-bit channells, with integer values in $[0,\ldots,255]$. hence, adding a Gaussian noise yields non-integer negative or values above 255, which is not  fully realistic: natural sampled  noise is  likely to be quantized in the  admissible values.