UTV Tools:Matlab Templates for Rank-Revealing UTV Decompositions

We describe a Matlab 5.2 package for computing and modifying certain rank-revealing decompositions that have found widespread use in signal processing and other applications. The package focuses on algorithms for URV and ULV decompositions, collectively known as UTV decompositions. We include algorithms for the ULLV decomposition, which generalizes the ULV decomposition to a pair of matrices. For completeness a few algorithms for computation of the RRQR decomposition are also included. The software in this package can be used as is, or can be considered as templates for specialized implementations on signal processors and similar dedicated hardware platforms

UTV Tools:Matlab Templates for Rank-Revealing UTV Decompositions

published in Numerical Algorithms and the paper's text is reprinted here by kind permissio

UTV Tools - Matlab Templates for Rank-Revealing UTV Decompositions

Contents 1 Introduction 1 2 Rank-Revealing Orthogonal Decompositions 3 2.1 The Singular Value Decomposition . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Numerical Rank and Singular Subspaces . . . . . . . . . . . . . . . . . . . . . 4 2.3 UTV Decompositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 A Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 UTV Algorithms 9 3.1 High-Rank Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2 Low-Rank Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.3 Refinement Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.4 Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4 Up- and Downdating 15 4.1 Updating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.2 Downdating . . . . . . . .

ULV-Based Signal Subspace Method for Speech Enhancement

In this paper the signal subspace approach for nonparametric speech enhancement is considered. Traditionally, the SVD (or the eigendecomposition) is used in frame-based methods to decompose the vector space of the noisy signal into a signal- and noise subspace [1, 2, 5]. Linear estimation of the clean signal from the information in the signal subspace is then performed using a set of nonparametric estimation criteria. In this paper, the rank-revealing ULV decomposition is used instead of the SVD, and we use recursive updating of the estimate instead of working in frames. An ULV formulation of three different estimation strategies is considered: Least Squares, Minimum Variance and Time Domain Constrained. Experiments indicate that the ULV-based algorithm is able to achieve the same quality of the reconstructed speech signal as the SVD-based method. 1 SIGNAL AND NOISE MODEL Let x = (x 1 ; x 2 ; \Delta \Delta \Delta ; xm ) T denote the noisy signal vector of m samples and assume that ..

Noise Reduction of Speech Signals using the Rank-Revealing ULLV Decomposition

A recursive approach for nonparametric speech enhancement is developed. The underlying principle is to decompose the vector space of the noisy signal into a signal subspace and a noise subspace. Enhancement is performed by removing the noise subspace and estimating the clean signal from the remaining signal subspace. The decomposition is performed by applying the rank-revealing ULLV algorithm to the noisy signal. With this formulation, a prewhitening operation becomes an integral part of the algorithm. Linear estimation is performed using a proposed minimum variance estimator. Experiments indicate that the approximative method is able to achieve a satisfactory quality of the reconstructed speech signal comparable with eigenfilter based methods. 1 INTRODUCTION Recently, a new approach for noise reduction of speech signals based on subspace decomposition has been proposed [1, 2, 4]. The idea is to organize the noisy speech signal in a Toeplitz structured data matrix, and to decompose t..