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  • Research Article
  • Open Access

The LOST Algorithm: Finding Lines and Separating Speech Mixtures

EURASIP Journal on Advances in Signal Processing20082008:784296

  • Received: 26 November 2007
  • Accepted: 2 July 2008
  • Published:


Robust clustering of data into linear subspaces is a frequently encountered problem. Here, we treat clustering of one-dimensional subspaces that cross the origin. This problem arises in blind source separation, where the subspaces correspond directly to columns of a mixing matrix. We propose the LOST algorithm, which identifies such subspaces using a procedure similar in spirit to EM. This line finding procedure combined with a transformation into a sparse domain and an L1-norm minimisation constitutes a blind source separation algorithm for the separation of instantaneous mixtures with an arbitrary number of mixtures and sources. We perform an extensive investigation on the general separation performance of the LOST algorithm using randomly generated mixtures, and empirically estimate the performance of the algorithm in the presence of noise. Furthermore, we implement a simple scheme whereby the number of sources present in the mixtures can be detected automatically.


  • Linear Subspace
  • Full Article
  • Blind Source Separation
  • Separation Performance
  • Publisher Note

Publisher note

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Authors’ Affiliations

Complex and Adaptive Systems Laboratory, University College Dublin, Belfield, Dublin, 4, Ireland
Hamilton Institute, National University of Ireland Maynooth, Co. Kildare, Ireland


© P. D. O’Grady and B. A. Pearlmutter 2008

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.