Explaining the parameterized wiener filter with alpha-stable processes

This paper introduces a new method for single-channel denoising that sheds new light on classical early developments on this topic that occurred in the 70's and 80's with Wiener filtering and spectral subtraction. Operating both in the short-Time Fourier transform domain, these methods consist in estimating the power spectral density (PSD) of the noise without speech. Then, the clean speech signal is obtained by manipulating the corrupted time-frequency bins thanks to these noise PSD estimates. Theoretically grounded when using power spectra, these methods were subsequently generalized to magnitude spectra, or shown to yield better performance by weighting the PSDs in the so-called parameterized Wiener filter. Both these strategies were long considered ad-hoc. To the best of our knowledge, while we recently proposed an interpretation of magnitude processing, there is still no theoretical result that would justify the better performance of parameterized Wiener filters. Here, we show how the α-stable probabilistic model for waveforms naturally leads to these weighted filters and we provide a grounded and fast algorithm to enhance corrupted audio that compares favorably with classical denoising methods.