Can we reconstructs a signal after it is being multiplied (not added) by a random noise (not with the normal distribution)?
Lets say I have S=10*sin(2*pi*5*t) for t=[0:.001:1] and I have a random noise V for the same time t. How Can I reconstruct S from X=S.*V (element wise product)?
Is is theoretically possible? I read this post about the Multiplicative noise but still I need help.
If the noise is truly random, doesn't mean that it can ruin the signal completely?
Background of my question: there is a machine learning method called "Non-negative matrix factorization" that can be used to find the components of a signal (assume signal is a combination of those components). I have seen this method as able to find the right components even after the combined signal was multiplied by a white noise!!