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A Linear Source Recovery Method for Underdetermined Mixtures of Uncorrelated AR-Model Signals Without Sparseness | IEEE Journals & Magazine | IEEE Xplore

A Linear Source Recovery Method for Underdetermined Mixtures of Uncorrelated AR-Model Signals Without Sparseness


Abstract:

Conventional sparseness-based approaches for instantaneous underdetermined blind source separation (UBSS) do not take into account the temporal structure of the source si...Show More

Abstract:

Conventional sparseness-based approaches for instantaneous underdetermined blind source separation (UBSS) do not take into account the temporal structure of the source signals. In this work, we exploit the source temporal structure and propose a linear source recovery solution for the UBSS problem which does not require the source signals to be sparse. Assuming the source signals are uncorrelated and can be modeled by an autoregressive (AR) model, the proposed algorithm is able to estimate the source AR coefficients from the mixtures given the mixing matrix. We prove that the UBSS problem can be converted into a determined problem by combining the source AR model together with the original mixing equation to form a state-space model. The Kalman filter is then applied to obtain a linear source estimate in the minimum mean-squared error sense. Simulation results using both synthetic AR signals and speech utterances show that the proposed algorithm achieves better separation performance compared with conventional sparseness-based UBSS algorithms.
Published in: IEEE Transactions on Signal Processing ( Volume: 62, Issue: 19, October 2014)
Page(s): 4947 - 4958
Date of Publication: 09 June 2014

ISSN Information:


I. Introduction

Blind SOURCE SEPARATION (BSS) refers to the recovery of the source signals from their mixtures without any knowledge of the mixing process or the signals [1]–[8]. Based on whether the mixing process is memoryless or not, BSS can be classified as instantaneous or convolutive mixing. The instantaneous mixing process can mathematically be expressed as {\bf x}[n]={\bf A}{\bf s}[n]+{\bf v}[n], \eqno{\hbox{(1)}}

where is a vector containing the mixtures, is a vector of source signals, is the mixing matrix, denotes the additive noise and is the discrete time index. In BSS, the objective is to estimate given . When , the problem is well-determined and can be solved using independent component analysis (ICA) [2]. However, when is non-invertible and this renders the underdetermined BSS (UBSS) a challenging problem.

References

References is not available for this document.