Multichannel high resolution NMF for modelling convolutive mixtures of non-stationary signals in the time-frequency domain

Several probabilistic models involving latent components have been proposed for modeling time-frequency (TF) representations of audio signals such as spectrograms, notably in the nonnegative matrix factorization (NMF) literature. Among them, the recent high-resolution NMF (HR-NMF) model is able to take both phases and local correlations in each frequency band into account, and its potential has been illustrated in applications such as source separation and audio inpainting. In this paper, HR-NMF is extended to multichannel signals and to convolutive mixtures. The new model can represent a variety of stationary and non-stationary signals, including autoregressive moving average (ARMA) processes and mixtures of damped sinusoids. A fast variational expectation-maximization (EM) algorithm is proposed to estimate the enhanced model. This algorithm is applied to piano signals, and proves capable of accurately modeling reverberation, restoring missing observations, and separating pure tones with close frequencies

MULTILINEAR SINGULAR VALUE DECOMPOSITION FOR STRUCTURED TENSORS

International audienceThe Higher-Order SVD (HOSVD) is a generalization of the Singular Value Decompo- sition (SVD) to higher-order tensors (i.e. arrays with more than two indices) and plays an important role in various domains. Unfortunately, this decomposition is computationally demanding. Indeed, the HOSVD of a third-order tensor involves the computation of the SVD of three matrices, which are referred to as "modes", or "matrix unfoldings". In this paper, we present fast algorithms for computing the full and the rank-truncated HOSVD of third-order structured (symmetric, Toeplitz and Hankel) tensors. These algorithms are derived by considering two specific ways to unfold a structured tensor, leading to structured matrix unfoldings whose SVD can be efficiently computed1

ADAPTIVE MULTILINEAR SVD FOR STRUCTURED TENSORS

International audienceThe Higher-Order SVD (HOSVD) is a generalization of the SVD to higher-order tensors (ie. arrays with more than two indexes) and plays an important role in various domains. Unfortunately, the computational cost of this decomposition is very high since the basic HOSVD algorithm involves the computation of the SVD of three highly redundant block-Hankel matrices, called modes. In this paper, we present an ultra-fast way of computing the HOSVD of a third-order structured tensor. The key result of this work lies in the fact it is possible to reduce the basic HOSVD algorithm to the computation of the SVD of three non-redundant Hankel matrices whose columns are multiplied by a given weighting function. Next, we exploit an FFT-based implementation of the orthogonal iteration algorithm in an adaptive way. Even though for a square (I ×I ×I) tensor the complexity of the basic full-HOSVD is O(I4) and O(rI3) for its r-truncated version, our approach reaches a linear complexity of O(rI log2(I))

Calculation of an entropy-constrained quantizer for exponentially damped sinudoids parameters

Technical report, 5 pagesThe Exponentially Damped Sinusoids (EDS) model can efficiently represent real-world audio signals. In the context of low bit rate parametric audio coding, the EDS model could bring a significant improvement over classical sinusoidal models. The inclusion of an additional damping parameter calls for a specific quantization scheme. In this report, we describe a new joint-scalar quantization scheme for EDS parameters in high resolution hypothesis, which is much easier to implement than a vector quantization scheme. A performance evaluation of this quantizer in comparison with a 3-dimensional vector quantizer is proposed in a paper submitted to IEEE Signal Processing Letters named "Entropy-Constrained Quantization of Exponentially Damped Sinusoids Parameters"

Entropy-constrained quantization of exponentially damped sinusoids parameters

International audienceSinusoidal modeling is traditionally one of the most popular techniques for low bitrate audio coding. Usually, the sinusoidal parameters are kept constant within a time segment but the exponentially damped sinusoidal (EDS) model is also an efficient alternative. However, the inclusion of an additional damping parameter calls for a specific quantization scheme. In this paper, we propose an asymptotically optimal entropy-constrained quantization method for amplitude, phase and damping parameters. We show that this scheme is nearly optimal in terms of rate-distortion trade-off. We also show that damping consumes the smallest part of the total entropy of quantization indexes, which suggests that the EDS model is truly efficient for audio coding

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

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