  We investigate the retrieval of a binary time-frequency mask from a few
observations of filtered white ambient noise. Confirming household wisdom in
acoustic modeling, we show that this is possible by inspecting the average
spectrogram of ambient noise. Specifically, we show that the lower quantile of
the average of $\mathcal{O}(\log(|\Omega|/\varepsilon))$ masked spectrograms is
enough to identify a rather general mask $\Omega$ with confidence at least
$\varepsilon$, up to shape details concentrated near the boundary of $\Omega$.
As an application, the expected measure of the estimation error is dominated by
the perimeter of the time-frequency mask. The estimator requires no knowledge
of the noise variance, and only a very qualitative profile of the filtering
window, but no exact knowledge of it.
