Estimate $s$ from $y=s+n$
I think you are seeking for an algorithm but this may help. If you don't know how $ s $ is distributed but you know its moments of first and second order, you can try with the linear estimator of the linear Minimum-mean Square Error (lmmse), with the following form,
$$
\hat{s}(y) = ay + b
$$
with
$$
a = \frac{ \mathrm{C}_{xy} }{ \sigma_{y}^{2} } \\
b = m_{s} - am_{y}
$$
where $ m $ denotes mean, $ \sigma $ variance and $ C $ covariance. It would help to know the moments of the noise, I mean, for example if is zero-mean and normalized to unity.