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Publication# A Tractable Framework for Estimating and Combining Spectral Source Models for Audio Source Separation

Abstract

The underdetermined blind audio source separation (BSS) problem is often addressed in the time-frequency (TF) domain assuming that each TF point is modeled as an independent random variable with sparse distribution. On the other hand, methods based on structured spectral model, such as the Spectral Gaussian Scaled Mixture Models (Spectral-GSMMs) or Spectral Non-negative Matrix Factorization models, perform better because they exploit the statistical diversity of audio source spectrograms, thus allowing to go beyond the simple sparsity assumption. However, in the case of discrete state-based models, such as Spectral-GSMMs, learning the models from the mixture can be computationally very expensive. One of the main problems is that using a classical Expectation-Maximization procedure often leads to an exponential complexity with respect to the number of sources. In this paper, we propose a framework with a linear complexity to learn spectral source models (including discrete state-based models) from noisy source estimates. Moreover, this framework allows combining different probabilistic models that can be seen as a sort of probabilistic fusion. We illustrate that methods based on this framework can significantly improve the BSS performance compared to the state-of-the-art approaches. (c) 2012 Elsevier B.V. All rights reserved.

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Related concepts (2)

Time–frequency analysis

In signal processing, time–frequency analysis comprises those techniques that study a signal in both the time and frequency domains simultaneously, using various time–frequency representations. Rather than viewing a 1-dimensional signal (a function, real or complex-valued, whose domain is the real line) and some transform (another function whose domain is the real line, obtained from the original via some transform), time–frequency analysis studies a two-dimensional signal – a function whose domain is the two-dimensional real plane, obtained from the signal via a time–frequency transform.

Sparse matrix

In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse but a common criterion is that the number of non-zero elements is roughly equal to the number of rows or columns. By contrast, if most of the elements are non-zero, the matrix is considered dense. The number of zero-valued elements divided by the total number of elements (e.