EURASIP Journal on Applied Signal Processing 
Volume 2006 (2006), Article ID 71632, 11 pages
doi:10.1155/ASP/2006/71632

Geometrical Interpretation of the PCA Subspace Approach for Overdetermined Blind Source Separation

S. Winter,1,2 H. Sawada,1 and S. Makino1

 1Department of Multimedia Communication and Signal Processing, University of Erlangen-Nuremberg, Erlangen 91058, Germany
2NTT Communication Science Laboratories, NTT Corporation, 2-4 Hikaridai Seika-cho, Soraku-gun, Kyoto 619-0237, Japan
Received 25 January 2005; Revised 24 May 2005; Accepted 26 August 2005

Abstract

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.