Acoustic blind source separation in reverberant and noisy environments [Elektronische Ressource] / vorgelegt von Robert Aichner

Robert Aichner

Informations

• Publié par: friedrich-alexander-universitat_erlangen-nurnberg
• Publié le: 01 janvier 2007
• Nombre de lectures: 9
• Langue: English
• Poids de l'ouvrage: 3 Mo

Extrait

Acoustic Blind Source Separation in
Reverberant and Noisy Environments
Der Technischen Fakultat der¨
Friedrich-Alexander-Universita¨t Erlangen-Nu¨rnberg
zur Erlangung des Grades
Doktor-Ingenieur
vorgelegt von
Robert Aichner
Erlangen, 2007Als Dissertation genehmigt von
der Technischen Fakultat der¨
Friedrich-Alexander-Universitat¨
Erlangen-Nu¨rnberg
Tag der Einreichung: 10. Mai 2007
Tag der Promotion: 24. Juli 2007
Dekan: Prof. Dr.-Ing. Alfred Leipertz
Berichterstatter: Prof. Dr.-Ing. Walter Kellermann
Prof. Dr. Dr. Bastiaan KleijnAcknowledgments
I wish to express my sincere gratitude to my advisor Prof. Dr.-Ing. Walter Kellermann
from the Friedrich-Alexander University in Erlangen, Germany, for giving me the oppor-
tunity to pursue my scientific interests at his research group and forhis constant support,
mentoring and feedback. I am grateful to Prof. Dr. Dr. Bastiaan Kleijn from the Royal
Institute of Technology in Stockholm, Sweden for dedicating a large portion of his busy
schedule to the review of this thesis and also for the possibility to spend two months as
a visiting researcher at his laboratory. I want to thank Prof. Dr.-Ing. Wolfgang Koch
and Prof. Dr.-Ing. Joachim Hornegger, all from the Friedrich-Alexander University in
Erlangen for showing so much interest in my work and for participating in the defense of
this thesis.
I am very indebted to my former colleague and office mate Herbert Buchner who
significantly contributed to the successful completion of this thesis by the uncountable,
fruitful, and very inspiring discussions I had with him. I am also grateful to all my
other colleagues, who made this laboratory such an interesting and enjoyable place to
work. I am thankful to the supportive staff, in particular to Mrs. Ursula Arnold and
Mrs. Ute Hespelein for their help to cope with all the administrative tasks and to Mr.
ManfredLindnerandMr. Ru¨digerNa¨gelforconstructingthemicrophonearrayhardware.
My appreciation also goes to all the students who have worked with me. Here, I am
particularly grateful to Fei Yan for his commitment during the realization of a real-time
blind source separation system.
I am also grateful to Prof. Dr. Shoji Makino from the NTT Communication Sci-
ence Laboratories, Kyoto, Japan for giving me the opportunity to conduct research at
his laboratory for my diploma thesis required by the University of Applied Sciences in
Regensburg, Germany. He and his colleagues have sparked my interest in blind source
separation and laid the foundations for this dissertation.
I wish to thank the European Union for partially funding this work by grants within
the projects “Audio eNhancemnt In secured Telecommunications Applications (ANITA)”
(FP5,IST-2001-34327)and“HearingintheCommunicationSociety(HEARCOM)”(FP6,
Project 004171).
Finally, I want to thank my family and all of my friends for their continuous encour-
agement and for sharing many unforgettable moments with me. Last but not least I want
to express my deepest gratitude tomy wife Yuri who patiently supported and encouraged
me throughout these years even during the early days we had to spend so far apart.v
Contents
1 Introduction 1
2 Acoustic Blind Source Separation Model 5
2.1 Instantaneous mixing model . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Convolutive mixing model . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 Point sources in free-field environments . . . . . . . . . . . . . . . . 8
2.2.2 Point sources in reverberant environments . . . . . . . . . . . . . . 11
2.2.3 Diffuse sound fields . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.4 Characterizing sound fields by the magnitude squared coherence
function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.4.1 Estimating the magnitude squared coherence function . . 20
2.2.4.2 Magnitude squared coherence of point sources . . . . . . . 23
2.2.4.3 Magnitude squared coherence of diffuse sound fields . . . . 26
2.2.5 Effects of sensor imperfections and positioning . . . . . . . . . . . . 28
2.3 Source signal characteristics and their utilization in blind source separation 29
2.4 Ambiguities in instantaneous and convolutive blind source separation . . . 32
2.5 Performance measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3 A Blind Source Separation Framework for Reverberant Environments 39
3.1 Optimum solution for blind source separation . . . . . . . . . . . . . . . . 40
3.1.1 Overall system matrix . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.1.2 Optimum BSS solution and resulting optimum demixing filter length 42
3.1.3 Optimum BSS demixing system and relationship to blind MIMO
identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.1.4 Constraining the optimum BSS solution to additionally minimize
output signal distortions . . . . . . . . . . . . . . . . . . . . . . . . 47
3.1.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2 Broadband versus narrowband optimization . . . . . . . . . . . . . . . . . 48
3.3 Generic time-domain optimization criterion and algorithmic framework . . 52vi Contents
3.3.1 Matrix formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.3.2 Optimization criterion . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.3.3 Gradient of the optimization criterion . . . . . . . . . . . . . . . . . 57
3.3.4 Equivariance property and natural gradient update . . . . . . . . . 61
3.3.5 Covariance versus correlation method . . . . . . . . . . . . . . . . . 63
3.3.6 Efficient Sylvester Constraint realizations and resulting initializa-
tion methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.3.7 Approximations leading to known and novel algorithms . . . . . . . 73
3.3.7.1 Higher-orderstatisticsrealizationbasedonmultivariatepdfs 74
3.3.7.2 Second-order statistics realization based on the multivari-
ate Gaussian pdf . . . . . . . . . . . . . . . . . . . . . . . 78
3.3.7.3 Realizations based on univariate pdfs . . . . . . . . . . . . 79
3.3.8 Efficient normalization and regularization strategies . . . . . . . . . 81
3.3.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.4 Broadband and narrowband DFT-domain algorithms . . . . . . . . . . . . 86
3.4.1 Broadband and narrowband signal model . . . . . . . . . . . . . . . 86
3.4.2 Equivalent formulation of broadband algorithms in the DFT domain 92
3.4.2.1 Signal model expressed by Toeplitz matrices . . . . . . . . 92
3.4.2.2 Iterative update rule in the DFT domain . . . . . . . . . . 93
3.4.2.3 DFT representation of the Sylvester matrix W and the
˜output signal Toeplitz matrices Y andY . . . . . . . . . 94
3.4.2.4 Higher-orderstatisticsrealizationbasedonmultivariatepdfs 98
3.4.2.5 Second-order statistics realization based on the multivari-
ate Gaussian pdf . . . . . . . . . . . . . . . . . . . . . . . 100
3.4.3 Selective approximations leading to well-known and novel algorithms102
3.4.3.1 Narrowband normalization and regularization strategies . 102
3.4.3.2 BSS based on higher-order statistics . . . . . . . . . . . . 107
3.4.3.3 BSS based on second-order statistics . . . . . . . . . . . . 116
3.4.3.4 Relationship of narrowband second-order BSS and the
magnitude-squared coherence function . . . . . . . . . . . 117
3.4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
3.5 Algorithm formulation for different update strategies . . . . . . . . . . . . 123
3.5.1 Offline update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
3.5.2 Online update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
3.5.3 Block-online update. . . . . . . . . . . . . . . . . . . . . . . . . . . 125
3.5.4 Adaptive stepsize techniques for block-online updates . . . . . . . . 127
3.6 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
3.6.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
3.6.2 Sylvester constraintSC and its efficient implementations . . . . . . 129Contents vii
3.6.3 Block-based estimation using covariance or correlation method . . . 131
3.6.4 Block-online adaptation and adaptive stepsize . . . . . . . . . . . . 133
3.6.5 Comparison of different HOS and SOS realizations . . . . . . . . . 135
3.6.6 Influence of reverberation time and source-sensor distance . . . . . 140
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
4 Extensions for Blind Source Separation in Noisy Environments 147
4.1 Pre-processing for noise-robust adaptation . . . . . . . . . . . . . . . . . . 148
4.1.1 Bias-removal techniques . . . . . . . . . . . . . . . . . . . . . . . . 149
4.1.1.1 Single-channel noise reduction . . . . . . . . . . . . . . . . 150
4.1.1.2 Multi-channel bias removal . . . . . . . . . . . . . . . . . 151
4.1.2 Subspace methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
4.2 Post-processing for suppression of residual crosstalk and background noise 155
4.2.1 Spectral weighting function for a single-channel postfilter . . . . . . 157
4.2.2 Estimation of residual crosstalk and background noise . . . . . . . . 160
4.2.2.1 Model of r