Separating More Sources Than Sensors Using Time-Frequency Distributions

Nguyen Linh-Trung,Karim Abed-Meraim,Adel Belouchrani,Boualem Boashash

doi:10.1155/asp.2005.2828

Abstract

We examine the problem of blind separation of nonstationary sources in the underdetermined case, where there are more sources than sensors. Since time-frequency (TF) signal processing provides effective tools for dealing with nonstationary signals, we propose a new separation method that is based on time-frequency distributions (TFDs). The underlying assumption is that the original sources are disjoint in the time-frequency (TF) domain. The successful method recovers the sources by performing the following four main procedures. First, the spatial time-frequency distribution (STFD) matrices are computed from the observed mixtures. Next, the auto-source TF points are separated from cross-source TF points thanks to the special structure of these mixture STFD matrices. Then, the vectors that correspond to the selected auto-source points are clustered into different classes according to the spatial directions which differ among different sources; each class, now containing the auto-source points of only one source, gives an estimation of the TFD of this source. Finally, the source waveforms are recovered from their TFD estimates using TF synthesis. Simulated experiments indicate the success of the proposed algorithm in different scenarios. We also contribute with two other modified versions of the algorithm to better deal with auto-source point selection.

Highlights

Blind source separation (BSS) considers the estimation of multiple sources from multiple observations received by a set of sensors, where the observations have been linearly mixed by the transfer medium
By extending the above-mentioned TF approach, we propose here a TF-based underdetermined blind source separation (UBSS) (TF-UBSS) algorithm for nonstationary sources under the main assumption that the sources are disjoint in the TF domain
As an alternative to using the modified Wigner-Ville distribution (MWVD) as proposed in the previous section for enhancing the auto-source point selection procedure, we propose another solution that is based on image processing, by using a component-extraction procedure

Summary

Introduction

Blind source separation (BSS) considers the estimation of multiple sources from multiple observations (mixtures) received by a set of sensors, where the observations have been linearly mixed by the transfer medium. The term “blind” indicates that no a priori knowledge of both the sources and the structure of the transfer medium is available. To compensate for this lack of information, the sources are usually assumed to be statistically independent [1]. BSS is important when precise modeling of the medium transfer is difficult or when no a priori information is available about the mixtures. BSS is known as blind array processing, signal copy, independent component analysis, or waveform preserving estimation. Typical examples of BSS are seen in (i) radar and sonar applications (source separation/recognition from antenna arrays, robust source localization from ill-calibrated arrays [6]), (ii) communications (multiuser detection [7]),

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Discussion

Conclusion