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Open Access

Separating More Sources Than Sensors Using Time-Frequency Distributions

  • Nguyen Linh-Trung1Email author,
  • Adel Belouchrani2,
  • Karim Abed-Meraim3 and
  • Boualem Boashash4
EURASIP Journal on Advances in Signal Processing20052005:845079

Received: 8 July 2004

Published: 23 October 2005


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.

Keywords and phrases

underdetermined blind source separationspatial time-frequency distributiontime-frequency synthesisunsupervised vector clusteringnonstationary sources

Authors’ Affiliations

Service Système Télécommunications Spatiales, Centre National d' Études Spatiales, Toulouse, France
Département d' Électronique, École Nationale Polytechnique, EL Harrach, Algiers, Algeria
Département Traîtement du Signal et des Images, École Nationale Supérieure des Télécommunications, Paris Cedex 13, France
College of Engineering, University of Sharjah, Sharjah, United Arab Emirates


© Linh-Trung et al. 2005