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Geometrical Interpretation of the PCA Subspace Approach for Overdetermined Blind Source Separation
EURASIP Journal on Advances in Signal Processing volume 2006, Article number: 071632 (2006)
We discuss approaches for blind source separation where we can use more sensors than sources to obtain a better performance. The discussion focuses mainly on reducing the dimensions of mixed signals before applying independent component analysis. We compare two previously proposed methods. The first is based on principal component analysis, where noise reduction is achieved. The second is based on geometric considerations and selects a subset of sensors in accordance with the fact that a low frequency prefers a wide spacing, and a high frequency prefers a narrow spacing. We found that the PCA-based method behaves similarly to the geometry-based method for low frequencies in the way that it emphasizes the outer sensors and yields superior results for high frequencies. These results provide a better understanding of the former method.
Hyvärinen A, Karhunen J, Oja E: Independent Component Analysis. John Wiley & Sons, New York, NY, USA; 2001.
Joho M, Mathis H, Lambert RH: Overdetermined blind source separation: using more sensors than source signals in a noisy mixture. Proceedings of 2nd International Conference on Independent Component Analysis and Blind Signal Separation (ICA '00), June 2000, Helsinki, Finland 81–86.
Westner A, Bove VM Jr.: Blind separation of real world audio signals using overdetermined mixtures. Proceedinds of 1st International Conference on Independent Component Analysis and Blind Signal Separation (ICA '99), January 1999, Aussois, France
Koutras A, Dermatas E, Kokkinakis G: Improving simultaneous speech recognition in real room environments using overdetermined blind source separation. Proceedings of 7th European Conference on Speech Communication and Technology (Eurospeech '01), September 2001, Aalborg, Denmark 1009–1012.
Asano F, Ikeda S, Ogawa M, Asoh H, Kitawaki N: Combined approach of array processing and independent component analysis for blind separation of acoustic signals. IEEE Transactions on Speech and Audio Processing 2003, 11(3):204–215. 10.1109/TSA.2003.809191
Sawada H, Araki S, Mukai R, Makino S: Blind source separation with different sensor spacing and filter length for each frequency range. Proceedings of 12th IEEE International Workshop on Neural Networks for Signal Processing (NNSP '02), September 2002, Martigny, Switzerland 465–474.
Winter S, Sawada H, Makino S: Geometrical understanding of the PCA subspace method for overdetermined blind source separation. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP~'03), April 2003, Hong Kong 2: 769–772.
Sawada H, Mukai R, Araki S, Makino S: Frequency-domain blind source separation. In Speech Enhancement. Edited by: Benesty J, Makino S, Chen J. Springer, Berlin, Germany; 2005:299–327.
Bingham E, Hyvärinen A: A fast fixed-point algorithm for independent component analysis of complex valued signals. International Journal of Neural Systems 2000, 10(1):1–8.
Ikram MZ, Morgan DR: Exploring permutation inconsistency in blind separation of speech signals in a reverberant environment. Proceedinds of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '00), June 2000, Istanbul, Turkey 2: 1041–1044.
Sawada H, Mukai R, Araki S, Makino S: A robust and precise method for solving the permutation problem of frequency-domain blind source separation. IEEE Transactions on Speech and Audio Processing 2004, 12(5):530–538. 10.1109/TSA.2004.832994
Hyvärinen A, Särelä J, Vigário R: Bumps and spikes: artifacts generated by independent component analysis with insufficient sample size. Proceedings of 1st International Workshop on Independent Component Analysis and Blind Signal Separation (ICA '99), January 1999, Aussois, France 425–429.
Nadal JP, Korutcheva E, Aires F: Blind source separation in the presence of weak sources. Neural Networks 2000, 13(6):589–596. 10.1016/S0893-6080(00)00041-1
Pillai SU: Array Signal Processing. Springer, New York, NY, USA; 1989.
Real World Computing Partnership : RWCP sound scene database in real acoustic environments. https://doi.org/tosa.mri.co.jp/sounddb/indexe.htm
Bronstein IN, Semendjajew KA, Musiol G, Mühlig H: Taschenbuch der Mathematik. 3rd edition. Harri Deutsch, Frankfurt am Main, Germany; 1997.
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Winter, S., Sawada, H. & Makino, S. Geometrical Interpretation of the PCA Subspace Approach for Overdetermined Blind Source Separation. EURASIP J. Adv. Signal Process. 2006, 071632 (2006). https://doi.org/10.1155/ASP/2006/71632
- Principal Component Analysis
- Information Technology
- Quantum Information
- Independent Component
- Noise Reduction