Publication

Nonnegative Matrix Factorization and Spatial Covariance Model for Under-Determined Reverberant Audio Source Separation

Pierre Vandergheynst, Rémi Gribonval
2010
Conference Papers

Abstract

We address the problem of blind audio source separation in the under-determined and convolutive case. The contribution of each source to the mixture channels in the time-frequency domain is modeled by a zero-mean Gaussian random vector with a full rank covariance matrix composed of two terms: a variance which represents the spectral properties of the source and which is modeled by a nonnegative matrix factorization (NMF) model and another full rank covariance matrix which encodes the spatial properties of the source contribution in the mixture. We address the estimation of these parameters by maximizing the likelihood of the mixture using an expectation-maximization (EM) algorithm. Theoretical propositions are corroborated by experimental studies on stereo reverberant music mixtures.

Official source

https://infoscience.epfl.ch/entities/publication/980863b2-6b6e-41a9-885b-1fb04c6b94ae

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Pierre Vandergheynst, Rémi Gribonval
2010
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/980863b2-6b6e-41a9-885b-1fb04c6b94ae

About this result

Related concepts (25)

Nonnegative matrix

In mathematics, a nonnegative matrix, written is a matrix in which all the elements are equal to or greater than zero, that is, A positive matrix is a matrix in which all the elements are strictly greater than zero. The set of positive matrices is a subset of all non-negative matrices. While such matrices are commonly found, the term is only occasionally used due to the possible confusion with positive-definite matrices, which are different. A matrix which is both non-negative and is positive semidefinite is called a doubly non-negative matrix.

Eigenvalues and eigenvectors

In linear algebra, an eigenvector (ˈaɪgənˌvɛktər) or characteristic vector of a linear transformation is a nonzero vector that changes at most by a constant factor when that linear transformation is applied to it. The corresponding eigenvalue, often represented by , is the multiplying factor. Geometrically, a transformation matrix rotates, stretches, or shears the vectors it acts upon. The eigenvectors for a linear transformation matrix are the set of vectors that are only stretched, with no rotation or shear.

Matrix decomposition

In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems. In numerical analysis, different decompositions are used to implement efficient matrix algorithms. For instance, when solving a system of linear equations , the matrix A can be decomposed via the LU decomposition.

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