Generalized Wiener filtering with fractional power spectrograms

International audienceIn the recent years, many studies have focused on the single-sensor separation of independent waveforms using so-called soft-masking strategies, where the short term Fourier transform of the mixture is multiplied element-wise by a ratio of spectrogram models. When the signals are wide-sense stationary, this strategy is theoretically justified as an optimal Wiener filtering: the power spectrograms of the sources are supposed to add up to yield the power spectrogram of the mixture. However, experience shows that using fractional spectrograms instead, such as the amplitude, yields good performance in practice, because they experimentally better fit the additivity assumption. To the best of our knowledge, no probabilistic interpretation of this filtering procedure was available to date. In this paper, we show that assuming the additivity of fractional spectrograms for the purpose of building soft-masks can be understood as separating locally stationary alpha-stable harmonizable processes, alpha-harmonizable in short, thus justifying the procedure theoretically

Proof of Wiener-like linear regression of isotropic complex symmetric alpha-stable random variables

This document features supplementary materials to the reference paper [1]. It provides the proof of equation (8) in [1]. This proof concerns a particular regression property of complex isotropic symmetric alpha-stable random variables (see [2]). In [1], this property is shown paramount in building efficient filters for separating symmetric alpha-stable processes. Such processes exhibit very large dynamic ranges while being locally stationary, and have been shown appropriate for audio modeling

Filtrage de Wiener généralisé pour des variables aléatoires positives alpha-stables

This report provides a mathematical proof of a result which is a generalization of Wiener filtering to Positive alpha-stable (PalphaS) distributions, a particular subclass of the alpha-stable distributions family whose support is [0;+inf[. PalphaS distributions are useful to model nonnegative data and since they are heavy-tailed, they present a natural robustness to outliers. In applications such as nonnegative source separation, it is paramount to have a way of estimating the isolated components that constitute a mixture. To address this issue, we derive an estimator of the sources which is given by the conditional expectation of the sources knowing the mixture. It extends the validity of the generalized Wiener filtering to PalphaS distributions. This allows us to extract the underlying PalphaS sources from their mixture

Sketching for nearfield acoustic imaging of heavy-tailed sources

International audienceWe propose a probabilistic model for acoustic source localization with known but arbitrary geometry of the microphone array. The approach has several features. First, it relies on a simple nearfield acoustic model for wave propagation. Second, it does not require the number of active sources. On the contrary, it produces a heat map representing the energy of a large set of candidate locations, thus imaging the acoustic field. Second, it relies on a heavy-tail alpha-stable probabilistic model, whose most important feature is to yield an estimation strategy where the multichannel signals need to be processed only once in a simple on- line procedure, called sketching. This sketching produces a fixed-sized representation of the data that is then analyzed for localization. The resulting algorithm has a small computational complexity and in this paper, we demonstrate that it compares favorably with state of the art for localization in realistic simulations of reverberant environments

Drum extraction in single channel audio signals using multi-layer non negative matrix factor deconvolution

International audienceIn this paper, we propose a supervised multilayer factorization method designed for harmonic/percussive source separation and drum extraction. Our method decomposes the audio signals in sparse orthogonal components which capture the harmonic content, while the drum is represented by an extension of non negative matrix factorization which is able to exploit time-frequency dictionaries to take into account non stationary drum sounds. The drum dictionaries represent various real drum hits and the decomposition has more physical sense and allows for a better interpretation of the results. Experiments on real music data for a harmonic/percussive source separation task show that our method outperforms other state of the art algorithms. Finally, our method is very robust to non stationary harmonic sources that are usually poorly decomposed by existing methods

Alpha-stable low-rank plus residual decomposition for speech enhancement

International audienceIn this study, we propose a novel probabilistic model for separating clean speech signals from noisy mixtures by decomposing the mixture spectrograms into a structured speech part and a more flexible residual part. The main novelty in our model is that it uses a family of heavy-tailed distributions, so called the α-stable distributions, for modeling the residual signal. We develop an expectation-maximization algorithm for parameter estimation and a Monte Carlo scheme for posterior estimation of the clean speech. Our experiments show that the proposed method outperforms relevant factorization-based algorithms by a significant margin

Cauchy Nonnegative Matrix Factorization

International audienceNonnegative matrix factorization (NMF) is an effective and popular low-rank model for nonnegative data. It enjoys a rich background, both from an optimization and probabilistic signal processing viewpoint. In this study, we propose a new cost-function for NMF fitting, which is introduced as arising naturally when adopting a Cauchy process model for audio waveforms. As we recall, this Cauchy process model is the only probabilistic framework known to date that is compatible with having additive magnitude spectrograms for additive independent audio sources. Similarly to the Gaussian power-spectral density, this Cauchy model features time-frequency nonnegative scale parameters, on which an NMF structure may be imposed. The Cauchy cost function we propose is optimal under that model in a maximum likelihood sense. It thus appears as an interesting newcomer in the inventory of useful cost-functions for NMF in audio. We provide multiplicative updates for Cauchy-NMF and show that they give good performance in audio source separation as well as in extracting nonnegative low-rank structures from data buried in very adverse noise

PROJET - Spatial Audio Separation Using Projections

International audienceWe propose a projection-based method for the unmixing of multi-channel audio signals into their different constituent spatial objects. Here, spatial objects are modelled using a unified framework which handles both point sources and diffuse sources. We then propose a novel methodology to estimate and take advantage of the spatial dependencies of an object. Where previous research has processed the original multichannel mixtures directly and has been principally focused on the use of inter-channel covariance structures, here we instead process projections of the multichannel signal on many different spatial directions. These linear combinations consist of observations where some spatial objects are cancelled or enhanced. We then propose an algorithm which takes these projections as the observations, discarding dependencies between them. Since each one contains global information regarding all channels of the original multichannel mixture, this provides an effective means of learning the parameters of the original audio, while avoiding the need for joint-processing of all the channels. We further show how to recover the separated spatial objects and demonstrate the use of the technique on stereophonic music signals