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Time-Domain Beamforming and Blind Source Separation Julien Bourgeois

Time-Domain Beamforming and Blind Source Separation By Julien Bourgeois

Time-Domain Beamforming and Blind Source Separation by Julien Bourgeois


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Summary

This book addresses the problem of separating spontaneous multi-party speech by way of microphone arrays (beamformers) and adaptive signal processing techniques. All experimental results have been obtained with real in-car microphone recordings involving simultaneous speech of the driver and the co-driver.

Time-Domain Beamforming and Blind Source Separation Summary

Time-Domain Beamforming and Blind Source Separation: Speech Input in the Car Environment by Julien Bourgeois

This book addresses the problem of separating spontaneous multi-party speech by way of microphone arrays (beamformers) and adaptive signal processing techniques. It is written is a concise manner and an effort has been made such that all presented algorithms can be straightforwardly implemented by the reader. All experimental results have been obtained with real in-car microphone recordings involving simultaneous speech of the driver and the co-driver.

Table of Contents

1 Introduction 1

1.1 Existing approaches: a brief overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Scope and objective of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Non-adaptive stationary beamforming 5

2.1 Problemand notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 The space-frequency response for omni-directional microphones . . . . . . . . . . . . . . . 6

2.3 Minimum VarianceDistortionless Response (MVDR) . . . . . . . . . . . . . . . . . . . . . 8

2.4 Data-independent beamformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.4.1 The delay-and-sumbeamformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.4.2 TheMVDR null beamformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.5 Statistically optimumMVDR beamformer . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.6 FromMVDR to Generalized Sidelobe Canceller (GSC) . . . . . . . . . . . . . . . . . . . . 12

2.7 The target signal cancellation problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.7.1 The power-inversion effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.7.2 Robust versions of the GSC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.8 Use of directionalmicrophones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.8.1 Directionalmicrophones with the same orientation . . . . . . . . . . . . . . . . . . 16

2.8.2 Directionalmicrophones oriented to the sources . . . . . . . . . . . . . . . . . . . . 16

2.9 Experiments under stationary acoustic conditions . . . . . . . . . . . . . . . . . . . . . . . 18<

2.9.1 Experiments with the mirror array . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.9.2 Experiments with the cocooning array . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.10 Summary and conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3 Implicit adaptation control for beamforming 27

3.1 Adaptive interference canceller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2 Implicit adaptation control with a pseudo-optimal step-size . . . . . . . . . . . . . . . . . 29

3.3 ILMS transient behavior and stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3.1 Transient convergence and divergence . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3.2 About the stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.4 Robustness improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.5.1 Experiments with the mirror array . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.5.2 Experiment with the cocooning array . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.6 Summary and conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4 Second-Order Blind Source Separation 43

4.1 Problemand notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.1.1 Froma scalar to a convolutivemixture model . . . . . . . . . . . . . . . . . . . . . 44

4.1.2 Separation constraints and degrees of freedom. . . . . . . . . . . . . . . . . . . . . 46

4.2 Nonstationarity and source separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.2.1 The insufficiency of decorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

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4.2.2 Nonstationarity-based separation cost function. . . . . . . . . . . . . . . . . . . . . 47

4.3 Gradient-basedminimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.3.1 Standard gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.3.2 Natural gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.4 Natural gradient algorithmfor non-square systems . . . . . . . . . . . . . . . . . . . . . . 50

4.5 Summary and conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5 Implementation Issues in Blind Source Separation 53

5.1 Convolutive Natural Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.1.1 Gradient in the Sylvestermanifold . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.1.2 From matrices to z-transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.1.3 Self-closed and non-self-closed natural gradients . . . . . . . . . . . . . . . . . . . . 56

5.1.4 From z-transforms back to the time domain . . . . . . . . . . . . . . . . . . . . . . 57

5.1.5 Application to second-order BSS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.1.6 Discussion: Which natural gradient is best? . . . . . . . . . . . . . . . . . . . . . . 60

5.2 Online adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.2.1 Blockwise batch BSS algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.2.2 Sample-wise BSS algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.3 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.3.1 Experiments with the mirror array . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.3.2 Experiments with the cocooning array . . . . . . . . . . . . . . . . . . . . . . . . . 66

5.3.3 Comparison with other BSS algorithms in the frequency domain . . . . . . . . . . 66

5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

6 Blind Source Separation: Convergence and Stability 71

6.1 Global convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.1.1 Difficulty of a global convergence analysis . . . . . . . . . . . . . . . . . . . . . . . 72

6.1.2 Convergence analysis for a simplified algorithm . . . . . . . . . . . . . . . . . . . . 73

6.2 Local stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

6.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

7 Comparison of Beamforming and Blind Source Separation 77

7.1 System identification vs. interference cancellation . . . . . . . . . . . . . . . . . . . . . . . 77

7.2 Properties of the cost function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

7.2.1 Convergence of the gradient descent . . . . . . . . . . . . . . . . . . . . . . . . . . 80

7.2.2 Statistical efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

7.3 Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

7.3.1 NLMS complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

7.3.2 BSS complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

7.3.3 NLMS vs. BSS complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

7.3.4 Online BSS algorithm in the special case N =2 . . . . . . . . . . . . . . . . . . . . 86

7.4 Experimental comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

7.5 Summary and conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

8 Combining Blind Source Separation and Beamforming 91

8.1 Existing combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

8.2 BSS and geometric prior information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

8.2.1 Causality information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

8.2.2 Prior information on the source direction of arrival . . . . . . . . . . . . . . . . . . 93

8.2.3 Geometric information at the initialization . . . . . . . . . . . . . . . . . . . . . . 95

8.2.4 Geometric information as a soft constraint . . . . . . . . . . . . . . . . . . . . . . . 96

8.2.5 Geometric information as a preprocessing . . . . . . . . . . . . . . . . . . . . . . . 99

8.3 Combining BSS and the power criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

8.4 Combining BSS with geometric prior information and the power criterion . . . . . . . . . 102

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8.5 Experimental results on automatic speech recognition . . . . . . . . . . . . . . . . . . . . 104

8.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

A Experimental setups 109

A.1 Mirror array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

A.2 Cocooning array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

A.3 Acoustic characteristics of the car cabin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

B The RGSC according to Hoshuyama et al. 113

B.1 RGSC for the mirror array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

B.2 RGSC for the cocooning array. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

B.3 Experimental comparison: GSC vs. RGSC. . . . . . . . . . . . . . . . . . . . . . . . . . . 115

B.3.1 Mirror array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

B.3.2 Cocooning array. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

B.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

C Stability Analysis 119

C.1 Mixing and separationmodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

C.2 Linearization of the BSS updates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

C.3 Local stability conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

Bibliography 125

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Additional information

NPB9780387688350
9780387688350
0387688358
Time-Domain Beamforming and Blind Source Separation: Speech Input in the Car Environment by Julien Bourgeois
New
Hardback
Springer-Verlag New York Inc.
2009-04-14
225
N/A
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