Simple Violet

Blind source separation based on statistical independence and low-rank matrix decomposition Independent low-rank matrix analysis 3

2016926

1

BSSILRMAFDICAIVAISNMFILRMAILRMANMFILRMANMF1ILRMA2

BSSILRMAFDICAIVAISNMFILRMAILRMANMFILRMANMF1ILRMA3

audio source separation etc.

1/44

CD

4

2/4

25

FDICA, IVA, ILRMANMFTF NMF

CD

L-chR-ch

2-ch

1-ch

1-ch

CD5

3/46

6

4/4nonnegative matrix factorization: NMF

7

Amplitude

Amplitude()()()Time

: : :

TimeFrequency

Frequency

[Lee, 1999], [Lee, 2000], etc.

NMFNMFTVXTVTVNMF7

BSSILRMAFDICAIVAISNMFILRMAILRMANMFILRMANMF1ILRMA8

blind source separation: BSS

BSSICA[Comon, 1994]IVA[Hiroe, 2006], [Kim, 2006]BSS9

State-of-the-art

BSS

BSSBSSICAIVAIVAState-of-the-artBSS9

FDICA10

ICA

1212

Permutation Solver

12

Freq.TimeICAfrequency-domain ICA: FDICA

ICA[Smaragdis, 1998], [Sawada, 2004], [Saruwatari, 2006], etc.

FDICAICA10

FDICADOABSS200611FDICA+DOA [Saruwatari, 2006]DOA

ICADOA

DOA

DOA

DOASource 1Source 2

DOADOA1DOA11

FDICA

ABF [Araki, 2003]ABF0ABFFDICAFDICAICA12

12

1

1

12

FDICAABF [Araki, 2003] 13

BSS ABF TR = 0 msTR = 300 msTR = 0 msTR = 300 ms

BSS2006independent vector analysis: IVA

FDICAICA

14

[Hiroe, 2006], [Kim, 2006], [Kim, 2007]

1IVAICAIVA2214

FDICAIVAscore functionScore function: gradient

IVA

IVA15

15

[Kim, 2007]

IVA16

x1x2x1x2Higher-order correlationHigher-order dependency

16

IVAIVA1

17

17

IVANMFBSS2016independent low-rank matrix analysis: ILRMA

NMF

18FrequencyTime

Frequency

Time

FrequencyTime

FrequencyBasis

BasisTime

IVAILRMA

[Kitamura, 2015], [Kitamura, 2016]

18

NMFNMF111

NMF

19

19

NMFItakura-Saito NMF: ISNMF

NMF20

[Fvotte, 2009]

20

STFT

NMF21

ImaginaryReali.i.d.

0

21

NMF22

Frequency binTime frame

: 0

22

IVANMFBSS2016independent low-rank matrix analysis: ILRMA

IVA23FrequencyTime

Frequency

Time

FrequencyTime

FrequencyBasis

BasisTime

IVAILRMA

23

ILRMAILRMA

ILRMAIVA ILRMAIVAIVA1ILRMAIVA1ILRMANMFgiven24

ISNMFIVA

24

ILRMAILRMA [Kitamura, 2016]NMF

25

, 1 0

25

ILRMA

26

IVA

NMFNMF

IVANMF26

BSSILRMAFDICAIVAISNMFILRMAILRMANMFILRMANMF1ILRMA27

NMFNMFNMF

28Ozerov and Fevotte, 2010 NMFEM ,NMFArberet et al., 2010 NMFEM ,NMFOzerov et al., 2011 NMFEM ,NMFSawada et al., 2013NMF , NMFKitamura et al., 20161NMF ,NMF

NMFNMFNMFRsTVNMFRs1Rs1RsW28

NMF [Sawada, 2013]

NMF29

TimeFrequency

TimeFrequency

TimeFrequency

TimeFrequency

TimeFrequency

29

[Duong, 2010]Duong model

30

Source image

Wiener filter

30

1

1

31

1

31

1111

32

: :

A11NMF32

NMF1

1NMFILRMANMFILRMA33

1

2.

3.

ILRMA

33

IVANMFILRMAIVANMFIVANMFNMF1NMFIVANMF

34

IVA

NMF

NMF

34

FDICA1

ICAIVA11

NMFNMF

NMFILRMA1NMF

NMF

35

BSSILRMAFDICAIVAISNMFILRMAILRMANMFILRMANMF1ILRMA36

ILRMAILRMANMFIVA1NMF1NMF11137

38 SiSECRWCP 22FFT 512 ms 128 ms (1/4) 130ILRMA160ILRMA2 SDR

2 m

Source 1

5.66 cm50

50

Source 2

2 m

Source 1

5.66 cm60

60

Source 2Impulse response E2A(reverberation time: 300 ms)Impulse response JR2(reverberation time: 470 ms)

2300msSDR38

fort_minor-remember_the_name39

Sawadas MNMFIVAOzerovs MNMFOzerovs MNMF with random initializationSawadas MNMF initialized by proposed methodProposed method w/o partitioning functionProposed method with partitioning functionDirectional clusteringSawadas MNMFIVAOzerovs MNMFOzerovs MNMF with random initializationSawadas MNMF initialized by proposed methodProposed method w/o partitioning functionProposed method with partitioning functionDirectional clustering

Violin synth.

Vocals

Violin synth.

VocalsE2A300msJR2470ms

ultimate_nz_tour40E2A300msJR2470msSawadas MNMFIVAOzerovs MNMFOzerovs MNMF with random initializationSawadas MNMF initialized by proposed methodProposed method w/o partitioning functionProposed method with partitioning functionDirectional clustering

Sawadas MNMFIVAOzerovs MNMFOzerovs MNMF with random initializationSawadas MNMF initialized by proposed methodProposed method w/o partitioning functionProposed method with partitioning functionDirectional clustering

Guitar

Synth.

Guitar

Synth.

Ozerovs MNMF with random initialization

ultimate_nz_tour41

IVAOzerovs MNMFProposed method w/o partitioning functionProposed method with partitioning functionSawadas MNMF initialized by proposed methodSawadas MNMF

GuitarSynth.

NMF42 SiSEC22FFT 256 ms 128 ms (1/4) 12ILRMA14ILRMA2 SDR

Number of bases for each source ( )

Number of bases for each source ( )

Speaker 1Speaker 2

42

female3_liverec_1m43130ms250msSawadas MNMFIVAOzerovs MNMFOzerovs MNMF with random initializationSawadas MNMF initialized by proposed methodProposed method w/o partitioning functionProposed method with partitioning functionDirectional clustering

Sawadas MNMFIVAOzerovs MNMFOzerovs MNMF with random initializationSawadas MNMF initialized by proposed methodProposed method w/o partitioning functionProposed method with partitioning functionDirectional clustering

Speaker 1

Speaker 2

Speaker 1

Speaker 2

male3_liverec_1m44130ms250ms(a)Sawadas MNMFIVAOzerovs MNMFOzerovs MNMF with random initializationSawadas MNMF initialized by proposed methodProposed method w/o partitioning functionProposed method with partitioning functionDirectional clustering

Sawadas MNMFIVAOzerovs MNMFOzerovs MNMF with random initializationSawadas MNMF initialized by proposed methodProposed method w/o partitioning functionProposed method with partitioning functionDirectional clustering

Speaker 1

Speaker 2

Speaker 1

Speaker 2

NMF1

45

SiSEC: bearlin-roads__snip_85_9914 s16 kHz: acoustic_guit_main, bass, vocals3: MATLAB 8.3, Intel Core i7-4790 (3.6 GHz): 200

46IVAMNMFILRMA()ILRMA()91.64498.4121.0173.4

s

200MNMF

1 47

147

BSSPCAPCA1NMF

48

Mixing:

BSS[Kitamura, 2015]

24BSSPCA1NMF48

1NMFNMF

49

1

11222:

1NMFT49

50 SiSECRWCP 22 PCAIVA, PCA1NMF NMF1NMFFFT 128 ms 64 ms (1/2) 130 SDR

JR2: 470 ms

2 m

80

60

122.83 cm

24470ms128ms150

: ultimate nz tour, guitar and vocal5110

PCA + 2ch IVAPCA +2ch proposed method4ch proposed method with basis sharing4ch multichannel NMF

PCA + 2ch IVAPCA + 2ch proposed method4ch multichannel NMF4ch proposed method with basis sharing53.8 s67.6 s8307.1 s330.97 s

: 200

PCAIVA1NMFNMF1NMFPCANMFNMF51

BSSILRMAFDICAIVAISNMFILRMAILRMANMFILRMANMF1ILRMA52

IVANMFILRMAFDICAIVAILRMANMFILRMAIVANMF1ILRMA1ILRMAIVA53

1/3[Lee, 1999]: D. D. Lee and H. S. Seung, Learning the parts of objects by non-negative matrix factorization, Nature, vol. 401, pp. 788791, 1999.[Lee, 2000]: D. D. Lee and H. S. Seung, Algorithms for non-negative matrix factorization, in Proc. Adv. Neural Inform. Process. Syst., 2000, vol. 13, pp. 556562.[Smaragdis, 1998]: P. Smaragdis, Blind separation of convolved mixtures in the frequency domain, Neurocomputing, vol. 22, pp. 2134, 1998.[Sawada, 2004]: H. Sawada, R. Mukai, S. Araki, and S.Makino, Convolutive blind source separation for more than two sources in the frequency domain, in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., 2004, pp. III-885III-888.[Saruwatari, 2006]: H. Saruwatari, T. Kawamura, T. Nishikawa, A. Lee, and K. Shikano, Blind source separation based on a fast-convergence algorithm combining ICA and beamforming, IEEE Trans. Audio, Speech, Lang. Process., vol. 14, no. 2, pp. 666678, Mar. 2006.[Araki, 2003]: S. Araki, S. Makino, Y. Hinamoto, R. Mukai, T. Nishikawa, and H. Saruwatari, Equivalence between frequency-domain blind source separation and frequency-domain adaptive beamforming for convolutive mixtures, EURASIP Journal on Advances in Signal Process., vol. 2003, no. 11, pp. 110, 2003.[Hiroe, 2006]: A. Hiroe, Solution of permutation problem in frequency domain ICA using multivariate probability density functions, in Proc. Int. Conf. Independent Compon. Anal. Blind Source Separation, 2006, pp. 601608.54

2/3[Kim, 2006]: T. Kim, T. Eltoft, and T.-W. Lee, Independent vector analysis: An extension of ICA to multivariate components, in Proc. Int. Conf. Independent Compon. Anal. Blind Source Separation, 2006, pp. 165172.[Kim, 2007]: T. Kim, H. T. Attias, S.-Y. Lee, and T.-W. Lee, Blind source separation exploiting higher-order frequency dependencies, IEEE Trans. Audio, Speech, Lang. Process., vol. 15, no. 1, pp. 7079, 2007.[Kitamura, 2015]: D. Kitamura, N. Ono, H. Sawada, H. Kameoka, and H. Saruwatari, Efficient multichannel nonnegative matrix factorization exploiting rank-1 spatial model, in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., 2015, pp. 276280.[Kitamura, 2016]: D. Kitamura, H. Saruwatari, H. Kameoka, Y. Takahashi, K. Kondo and S. Nakamura, Determined blind source separation unifying independent vector analysis and nonnegative matrix factorization, IEEE/ACM Trans. Audio, Speech, Lang. Process., vol. 24, no. 9, pp. 16261641, Spt. 2016.[Fvotte, 2009]: C. Fvotte, N. Bertin, and J.-L.Durrieu, Nonnegative matrix factorization with the Itakura-Saito divergence. With application to music analysis, Neural Comput., vol. 21, no. 3, pp. 793830, 2009.[Sawada, 2013]: H. Sawada, H.Kameoka, S.Araki, and N. Ueda, Multichannel extensions of non-negative matrix factorization with complex-valued data, IEEE Trans. Audio, Speech, Lang. Process., vol. 21, no. 5, pp. 971982, May 2013.55

3/3[Duong, 2010]: N. Q. K. Duong, E. Vincent, and R. Gribonval, Under-determined reverberant audio source separation using a full-rank spatial covariance model, IEEE Trans. Audio, Speech, Lang. Process., vol. 18, no. 7, pp. 18301840, Sep. 2010.[Kitamura, 2015]: D. Kitamura, N. Ono, H. Sawada, H. Kameoka, and H. Saruwatari, Relaxation of rank-1 spatial constraint in overdetermined blind source separation, in Proc. Eur. Signal Process. Conf., 2015, pp. 12711275.

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