Noise Reduction with Optimal Variable Span Linear Filters

Research output: Contribution to journalJournal article

Abstract

In this paper, the problem of noise reduction is
addressed as a linear filtering problem in a novel way by using
concepts from subspace-based enhancement methods, resulting
in variable span linear filters. This is done by forming the filter
coefficients as linear combinations of a number of eigenvectors
stemming from a joint diagonalization of the covariance matrices
of the signal of interest and the noise. The resulting filters are flexible
in that it is possible to trade off distortion of the desired signal
for improved noise reduction. This tradeoff is controlled by the
number of eigenvectors included in forming the filter. Using these
concepts, a number of different filter designs are considered, like
minimum distortion, Wiener, maximum SNR, and tradeoff filters.
Interestingly, all these can be expressed as special cases of variable
span filters. We also derive expressions for the speech distortion
and noise reduction of the various filter designs. Moreover, we
consider an alternative approach, wherein the filter is designed
for extracting an estimate of the noise signal, which can then be
extracted from the observed signals, which is referred to as the
indirect approach. Simulations demonstrate the advantages and
properties of the variable span filter designs, and their potential
performance gain compared to widely used speech enhancement
methods.
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Details

In this paper, the problem of noise reduction is
addressed as a linear filtering problem in a novel way by using
concepts from subspace-based enhancement methods, resulting
in variable span linear filters. This is done by forming the filter
coefficients as linear combinations of a number of eigenvectors
stemming from a joint diagonalization of the covariance matrices
of the signal of interest and the noise. The resulting filters are flexible
in that it is possible to trade off distortion of the desired signal
for improved noise reduction. This tradeoff is controlled by the
number of eigenvectors included in forming the filter. Using these
concepts, a number of different filter designs are considered, like
minimum distortion, Wiener, maximum SNR, and tradeoff filters.
Interestingly, all these can be expressed as special cases of variable
span filters. We also derive expressions for the speech distortion
and noise reduction of the various filter designs. Moreover, we
consider an alternative approach, wherein the filter is designed
for extracting an estimate of the noise signal, which can then be
extracted from the observed signals, which is referred to as the
indirect approach. Simulations demonstrate the advantages and
properties of the variable span filter designs, and their potential
performance gain compared to widely used speech enhancement
methods.
Original languageEnglish
JournalI E E E Transactions on Audio, Speech and Language Processing
Volume24
Issue number4
Pages (from-to)631-644
ISSN1558-7916
DOI
StatePublished - Apr 2016
Publication categoryResearch
Peer-reviewedYes

    Research areas

  • joint diagonalization, noise reduction, optimal filters, span, speech enhancement, subspace

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