# Get noise model from true and distorted data

I have been given two data sets:

• Set A: a small data set containing data randomly drawn form an underlying distribution

• Set B: a very large data set containing data randomly drawn from the same distribution, however in the process it got distorted.

Furthermore information about the type of corruption has been given. It is additive noise which comes from a certain given distribution, however the parameters $\theta$ are missing, I would like to estimate these parameters.

Initially thought about estimating these parameters using maximum likelihood:

\begin{equation*} \hat{\theta} \in \arg \max_{\theta \in \Theta} \mathcal{L} (\theta | n) \end{equation*}

However, I have not been given the applied noise $n$ directly, and am not sure how to continue. I would greatly appreciate it if you could point me to any potential methods (or just literature) I can use to solve this problem.