EURASIP Journal on Advances in Signal Processing 
Volume 2007 (2007), Article ID 92953, 24 pages
doi:10.1155/2007/92953
Research Article

Subspace-Based Noise Reduction for Speech Signals via Diagonal and Triangular Matrix Decompositions: Survey and Analysis

Per Christian Hansen1 and Søren Holdt Jensen2

 1Informatics and Mathematical Modelling, Technical University of Denmark, Building 321, Lyngby 2800, Denmark
2Department of Electronic Systems, Aalborg University, Niels Jernes Vej 12, Aalborg 9220, Denmark
Received 1 October 2006; Revised 18 February 2007; Accepted 31 March 2007

Recommended by Marc Moonen

Abstract

We survey the definitions and use of rank-revealing matrix decompositions in single-channel noise reduction algorithms for speech signals. Our algorithms are based on the rank-reduction paradigm and, in particular, signal subspace techniques. The focus is on practical working algorithms, using both diagonal (eigenvalue and singular value) decompositions and rank-revealing triangular decompositions (ULV, URV, VSV, ULLV, and ULLIV). In addition, we show how the subspace-based algorithms can be analyzed and compared by means of simple FIR filter interpretations. The algorithms are illustrated with working Matlab code and applications in speech processing.