Estimation of binary time-frequency masks from ambient noise

TL;DR

This paper demonstrates that a binary time-frequency mask can be reliably estimated from ambient noise observations using spectrogram averaging, without detailed knowledge of noise variance or filtering profile.

Contribution

It introduces a method to identify general binary masks from ambient noise by analyzing average spectrograms, requiring minimal prior information.

Findings

The lower quantile of averaged spectrograms identifies the mask with high confidence.

Estimation error is primarily influenced by the perimeter of the mask.

The method does not require precise noise variance or filter profile knowledge.

Abstract

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.