Open Access

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

EURASIP Journal on Advances in Signal Processing20072007:092953

DOI: 10.1155/2007/92953

Received: 1 October 2006

Accepted: 31 March 2007

Published: 13 June 2007

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.

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Authors’ Affiliations

(1)
Informatics and Mathematical Modelling, Technical University of Denmark
(2)
Department of Electronic Systems, Aalborg University

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Copyright

© P. C. Hansen and S. H. Jensen. 2007

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.