R has a large number of random number generators to choose from.

https://cran.r-project.org/web/views/Distributions.html

If you want to sample from a law with distribution function F, then sample from at uniform distribution on [0,1] and apply F^(-1) to the result.

Yann Lanoiselée Thank for your anwser, I begin to work on the Monte-Carlo method, I will look at that.

Timothy A Ebert Thank you, but my noise generation is very particular and I think that no generator are now created for this kind of noise (Speckles noise)

Peter Harremoës Thank you too, I haven't try this simple , but the equation is pretty complicated and I think that the inverse function is not trivial. I will try it.

Speckles noise is generated in something like a radar image as radio waves interact with (amongst other things) the molecular irregularities on a surface.

All of the answers will involve a random number generator of some type. The difficulty is more in the application. So how about a cellular model where you have an initial image and each pixel is altered by a random value. The magnitude and variance of that value selected as appropriate to your goals. If you can identify specific sources of noise then the cellular model can be distorted according to a series of random numbers: The new value = original value + Gaussian(2,41) + Uniform(0,1)^Uniform(-2.7, 8.454734) + Gaussian(3,2)/sin(Uniform(0,180)). The complexity is limited only by relevant theory and your ability to justify more creative choices. You could model irregularities in the detector (say edge effects) using if-then statements or functions of random numbers that use positional information: + Gaussian(0,1)/2^(row number).