A Conceptual Framework for Noise Reduction

95 Pages·2015·1.161 MB·English

by  Jacob Benesty, Jingdong Chen (auth.)

SPRINGER BRIEFS IN
ELECTRICAL AND COMPUTER ENGINEERING
Jacob Benesty
Jingdong Chen
A Conceptual
Framework for
Noise Reduction
123
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Jacob Benesty Jingdong Chen
(cid:129)
A Conceptual Framework
for Noise Reduction
123
JacobBenesty Jingdong Chen
INRS-EMT,University ofQuebec Northwestern Polytechnical University
Montreal, QC Xi’an,Shaanxi
Canada China
ISSN 2191-8112 ISSN 2191-8120 (electronic)
SpringerBriefs inElectrical and Computer Engineering
ISBN 978-3-319-12954-9 ISBN 978-3-319-12955-6 (eBook)
DOI 10.1007/978-3-319-12955-6
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Abstract
The noise reduction (or speech enhancement) problem has been studied for
at least five decades but its understanding and the development of reliable
solutionsaremorethaneververywelcome.Therefore,byhavingasolidgrasp
of this problem, it will certainly become easier to design a well-targeted so-
lution for a well-defined application. In this work, we propose a conceptual
framework that can be applied to the many different aspects of noise reduc-
tion. As a consequence, the monaural or binaural noise reduction problem,
in the time domain or in the frequency domain, with a single microphone
or with multiple microphones, is presented in a unified way. Moreover, the
derivation of optimal linear filters is simplified as well as the performance
measures for their evaluation.
v
Contents
1 Introduction.............................................. 1
1.1 Noise Reduction........................................ 1
1.2 Organization of the Work................................ 2
References ................................................. 2
2 Conceptual Framework ................................... 3
2.1 Signal Model........................................... 3
2.2 Principle of the Conceptual Framework.................... 4
2.3 Performance Measures .................................. 6
2.4 Mean-Squared-Error (MSE) Based Criterion ............... 9
2.5 Summary.............................................. 12
References ................................................. 13
3 Single-Channel Noise Reduction in the Time Domain..... 15
3.1 Signal Model........................................... 15
3.2 Linear Filtering ........................................ 17
3.3 Performance Measures .................................. 18
3.4 MSE-Based Criterion ................................... 20
3.5 Optimal Filters ........................................ 22
3.6 Simulations............................................ 24
References ................................................. 30
4 Single-Channel Noise Reduction in the STFT Domain
with Interframe Correlation .............................. 31
4.1 Signal Model........................................... 31
4.2 Linear Filtering ........................................ 33
4.3 Performance Measures .................................. 34
4.4 MSE-Based Criterion ................................... 39
4.5 Optimal Filters ........................................ 41
4.6 Particular Case ........................................ 44
4.7 Simulations............................................ 44
vii
viii Contents
References ................................................. 50
5 Binaural Noise Reduction in the Time Domain ........... 51
5.1 Signal Model........................................... 51
5.2 Widely Linear Filtering ................................. 53
5.3 Performance Measures .................................. 56
5.4 MSE-Based Criterion ................................... 58
5.5 Optimal Filters ........................................ 61
5.6 Simulations............................................ 62
References ................................................. 65
6 Multichannel Noise Reduction in the STFT Domain...... 67
6.1 Signal Model........................................... 67
6.2 Linear Filtering ........................................ 70
6.3 Performance Measures .................................. 71
6.4 MSE-Based Criterion ................................... 75
6.5 Optimal Filters ........................................ 77
6.6 Simulations............................................ 81
References ................................................. 86
Index......................................................... 87
Chapter 1
Introduction
Inthischapter,weverybrieflyintroducetheproblemofnoisereduction.For
more details, the reader is invited to consult the rich literature on this topic.
1.1 Noise Reduction
Theproblemofnoisereduction(orspeechenhancement)isanimportantpart
ofspeechprocessing[1]andalltheideasdevelopedinthistopiccanbeeasily
applied to the general problem of signal enhancement. It is well known that
any speech communication system suffers from the ubiquitous presence of
additive noise [2], [3]. Typical examples of such products are cellular phones
andhearingaids.Inthesesystems,thenoisedegradestheperceptualquality
of the speech and will impair the speech intelligibility when the signal-to-
noise ratio (SNR) comes down to a certain level. Therefore, the objective
of noise reduction is to suppress such additive noise for purposes of speech
enhancement.
The first noise reduction algorithm was proposed by Schroeder more than
50yearsago[4],[5];itisbasicallythespectralmagnitudesubtractionmethod.
Since then a great deal of progress has been made. Not only we can better
exploit the temporal/spectral information of the signals but also the spa-
tial information by using multiple microphones. Thanks to the spatial in-
formation, we can better compromise between noise reduction and speech
distortion, which is a fundamental limitation of single-channel noise reduc-
tion algorithms. Even though today we have a better understanding of this
problem and some interesting solutions available, it is far from being solved.
Monauralorbinauralnoisereductioncanbeperformedinthetimedomain
or in the frequency domain, with one single microphone or with multiple
microphones. Very often, in the literature, most approaches seem to be very
different and their evaluation does not seem to be consistent. In this work,
we present a framework that has the potential to simplify the study of the
(cid:2)TheAuthor(s)2015 1
J.BenestyandJ.Chen,AConceptualFrameworkforNoiseReduction,
SpringerBriefsinElectricalandComputerEngineering,
DOI10.1007/978-3-319-12955-6_1
2 1 Introduction
general speech enhancement problem. Because of their great flexibility, we
limit this investigation to linear filters. Within the proposed framework, the
most important performance measures are derived as well as general forms
of the optimal filters.
1.2 Organization of the Work
This book consists of six chapters including this introduction. In Chapter 2,
wepresentaconceptualframeworkforstudyingthegeneralproblemofnoise
reduction. Furthermore, we introduce two important performance measures:
the speech intelligibility index and the speech quality index. In Chapters 3,
4, 5, and 6, we show how this concept is applied to the single-channel noise
reduction in time domain, to the single-channel noise reduction in the short-
timeFouriertransform(STFT)domain,tothebinauralnoisereductioninthe
time domain, and to the multichannel noise reduction in the STFT domain,
respectively.
References
1. J.Benesty,M.M.Sondhi,andY.Huang,Eds.,SpringerHandbookofSpeechProcess-
ing.Berlin,Germany:Springer-Verlag,2007.
2. J.Benesty,J.Chen,Y.Huang,andI.Cohen, Noise Reduction in Speech Processing.
Berlin,Germany:Springer-Verlag,2009.
3. P. Loizou, Speech Enhancement: Theory and Practice. Boca Raton, FL: CRC Press,
2007.
4. M.R.Schroeder,U.S.PatentNo.3,180,936,filedDec.1,1960,issuedApr.27,1965.
5. M.R.Schroeder,U.S.PatentNo.3,403,224,filedMay28,1965,issuedSept.24,1968.