After superimposing two sine functions with different frequencies, through Fourier transform, it is easy to know which sine functions with different frequencies are superimposed to form the superimposed function. So, here is my question, if I superimpose two 2D Gaussian noises with different means and standard deviations, is there any method to identify these two Gaussian noises just like Fourier transform?
I assume you mean you add two noise realizations together. There is no way to disambiguate them. Adding two normally-distributed noise realizations yields a new normally-distributed noise realization whose mean is the sum of the original two means, and whose standard deviation is the square root of the sum of the squares of the original two standard deviations.