"Estimation of binary time-frequency masks from ambient white noise"Speckbacher, MichaelTime-frequency masking plays a prominent role in many fields, in particular in acoustics, and much work has been put into identifying optimal masks for certain tasks. This talk will be concerned with a novel method for the inverse problem of identifying the binary mask $\chi_\Omega$ of a time-frequency localization operator $H_\Omega$. Our probabilistic method works as follows: take $K$ independent realizations of white noise $\mathcal{N}_k$ and calculate $\rho(z)=\frac{1}{K}\sum_k |V_g H_\Omega \mathcal{N}_k(z)|^2$. We then define an estimator of $\Omega$ by $$ \widehat{\Omega}=\{z\in\mathbb{R}^{2d}: \rho(z)/\|\rho\|_\infty\geq 1/4\}, $$ and show that (with high probability and in expectation) the performance of this method in terms of the symmetric difference of $\Omega$ and $\widehat{\Omega}$ is comparable to the deterministic accumulated spectrograms method while exponentially outperforming it in terms of the number of functions that need to be calculated. It should be emphasized that our method does not require prior knowledge of the window of the localization operator or the variance of the ambient white noise. |
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