MITSUBISHI ELECTRIC RESEARCH LABORATORIES http://www.merl.com
Separation of Mixed Audio Sources by Independent Subspace Analysis
Michael A. Casey and Alex Westner
TR2001-31
September 2001
Abstract We propose the method of independent subspace analysis (ISA) for separating individual audio sources from a single-channel mixture. ISA is based on independent component analysis (ICA) but relaxes the constraint that requires at least as many mixture observation signals as sources. A second extension to ICA is the use of dynamic components to represent non-stationary signals. Sources are tracked by similarity of dynamic components over small time steps. We propose a method for grouping components by partitioning a matrix of independent component crossentropies that we call an ixegram. The ixegram measures the mutual similarities of components in an audio segment and clustering the ixegram yields the source subspaces and time trajectories. To demonstrate the techniques we give examples of ISA applied to separation of musical and speech sources from single-channel mixtures. Proceedings of the International Computer Music Conference, Berlin, August 2000
This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. c Mitsubishi Electric Research Laboratories, Inc., 2001 Copyright 201 Broadway, Cambridge, Massachusetts 02139
MERLCoverPageSide2
MERL – A MITSUBISHI ELECTRIC RESEARCH LABORATORY http://www.merl.com
Separation of Mixed Audio Sources by Independent Subspace Analysis
Michael A. Casey
TR-2001-31
September 2001
Abstract We propose the method of independent subspace analysis (ISA) for separating individual audio sources from a single-channel mixture. ISA is based on independent component analysis (ICA) but relaxes the constraint that requires at least as many mixture observation signals as sources. A second extension to ICA is the use of dynamic components to represent non-stationary signals. Sources are tracked by similarity of dynamic components over small time steps. We propose a method for grouping components by partitioning a matrix of independent component crossentropies that we call an ixegram. The ixegram measures the mutual similarities of components in an audio segment and clustering the ixegram yields the source subspaces and time trajectories. To demonstrate the techniques we give examples of ISA applied to separation of musical and speech sources from single-channel mixtures.
This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Information Technology Center America; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Information Technology Center America. All rights reserved. c Mitsubishi Electric Information Technology Center America, 2001 Copyright 201 Broadway, Cambridge, Massachusetts 02139
Proceedings of the International Computer Music Conference, Berlin, August 2000.
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dB scale
3200
−10
1600
−20
800
−30
400
−40
200
0.5
1
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−20
1600 −40
800 400
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100
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100
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6400
Frequency (Hz)
Frequency (Hz)
Filterbank: Extracted Snare Drum
0
6400
50
2
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1
1.5
Time (s)
Time (s)
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1
2
0.5
Amplitude
Amplitude
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−1
0
0.5
1
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−20
1600 −40
800 400
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100 0.5
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1
1.5
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2
2.5
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6400 3200
−20
1600 −40
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2
0.5
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Time (s)
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Signal Waveform
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2
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Time (s)
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scale 400
5 10
350
15
Component Index
300 20 250
25 30
200
35
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dB scale 0
Frequency (Hz)
6400 3200
−10
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Signal Waveform 1
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Filterbank: Extracted Speech
dB scale 0
6400
Frequency (Hz)
3200
−20
1600 −40
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Signal Waveform 1
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