Musical Source Separation: Principles and State of the Art

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1 Musical Surce Separatin: Principles and State f the Art Juan Jsé Burred Équipe Analyse/Synthèse, IRCAM burred@ircam.fr 2nd Internatinal Wrkshp n Learning Semantics f Audi Signals (LSAS), Paris, 21st June 2008

2 1. Intrductin Presentatin verview Paradigms, tasks, applicatins Mixing mdels 2. Slving the linear mixing mdel Jint and staged separatin 3. Estimatin f the mixing matrix The need fr sparsity Independent Cmpnent Analysis Clustering methds, ther methds 4. Estimatin f the surces Nrm minimizatin Time-frequency masking 5. Methds using advanced surce mdels Adaptive basis decmpsitin methds Sinusidal methds Supervised methds 6. Cnclusins Juan Jsé Burred. Musical Surce Separatin. 2

3 1. Intrductin Presentatin verview Paradigms, tasks, applicatins Mixing mdels 2. Slving the linear mixing mdel Jint and staged separatin 3. Estimatin f the mixing matrix The need fr sparsity Independent Cmpnent Analysis Clustering methds, ther methds 4. Estimatin f the surces Nrm minimizatin Time-frequency masking 5. Methds using advanced surce mdels Adaptive basis decmpsitin methds Sinusidal methds Supervised methds 6. Cnclusins Juan Jsé Burred. Musical Surce Separatin. 3

Sund Surce Separatin Ccktail party effect E. C. Cherry, 1953. Ability t cncentrate attentin n a specific sund surce frm within a mixture. Even when interfering energy is clse t energy f desired surce.

Prince Shtku Cmputer (Okun et al., 1997) Bth allegries imply an extra step f semantic understanding f the surces, beynd mere acustical islatin. [Cherry53] [Okun97] E. C. Cherry.

4 Sund Surce Separatin Ccktail party effect E. C. Cherry, Ability t cncentrate attentin n a specific sund surce frm within a mixture. Even when interfering energy is clse t energy f desired surce. Prince Shtku Challenge Legendary Japanese prince Shtku (6th Century AD) culd listen and understand simultaneusly the petitins by ten peple. Cncentrate attentin n several surces at the same time! Prince Shtku Cmputer (Okun et al., 1997) Bth allegries imply an extra step f semantic understanding f the surces, beynd mere acustical islatin. [Cherry53] [Okun97] E. C. Cherry. Sme Experiments n the Recgnitin f Speech, With One and Tw Ears. Jurnal f the Acustical Sciety f America, Vl. 25, H. G. Okun, T. Nakatani and T. Kawabata. Understanging Three Simultaneus Speeches. Prc. Int. Jint Cnference n Artificial Intelligence (IJCAI), Nagya, Japan, Juan Jsé Burred. Musical Surce Separatin. 4

5 The paradigms f Musical Surce Separatin (based n [Scheirer00]) Understanding withut separatin Multipitch estimatin, music genre classificatin Glass ceiling f traditinal methds (MFCC, GMM) [Aucuturier&Pachet04] Separatin fr understanding First (partially) separate, then feature extractin Surce separatin as a way t break the glass ceiling? Separatin withut understanding BSS: Blind Surce Separatin (ICA, ISA, NMF) Blind means: nly very general statistical assumptins taken. Understanding fr separatin Supervised surce separatin (based n a training database) [Scheirer00] [Aucuturier&Pachet04] E. D. Scheirer. Music-Listening Systems. PhD thesis, Massachusetts Institute f Technlgy, J.-J. Aucuturier and F. Pachet. Imprving Timbre Similarity: Hw High is the Sky? Jurnal f Negative Results in Speech and Audi Sciences, 1 (1), Juan Jsé Burred. Musical Surce Separatin. 5

6 Required sund quality Regarding the quality f the separated sunds, surce separatin tasks can be divided int: Audi Quality Oriented (AQO) Aimed at full unmixing at the highest pssible quality. Applicatins: Unmixing, remixing, upmixing Hearing aids Pst-prductin Significance Oriented (SO) Separatin quality just enugh fr facilitating semantic analysis f cmplex signals. Less demanding, mre realistic. Applicatins: Music Infrmatin Retrieval Plyphnic Transcriptin Object-based audi cding Juan Jsé Burred. Musical Surce Separatin. 6

7 Musical Surce Separatin Tasks Classificatin accrding t the nature f the mixtures: Classificatin accrding t available a priri infrmatin: Juan Jsé Burred. Musical Surce Separatin. 7

8 Linear mixing mdel Only amplitude scaling befre mixing (summing) Linear stere recrding setups: XY Stere MS Stere Clse miking Direct injectin Juan Jsé Burred. Musical Surce Separatin. 8

9 Delayed mixing mdel Amplitude scaling and delay befre mixing Delayed stere recrding setups: AB Stere Mixed Stere Clse miking with delay Direct injectin with delay Juan Jsé Burred. Musical Surce Separatin. 9

envirnment Binaural Clse miking with reverb Direct

10 Cnvlutive mixing mdel Filtering between surces and sensrs Cnvlutive stere recrding setups: Reverberant envirnment Binaural Clse miking with reverb Direct injectin with reverb Juan Jsé Burred. Musical Surce Separatin. 10

11 Sme terminlgy System f linear equatins: Usual algebraic methds frm high schl: X knwn, A knwn, S unknwn But in surce separatin: unknwn variables (S, surces) AND unknwn cefficients (A, mixing matrix) Algebra terminlgy is retained fr surce separatin: Mre equatins (mixtures) than unknwns (surces): verdetermined Same number f equatins (mixtures) than unknwns (surces): determined (square A) Less equatins (mixtures) than unknwns (surces): underdetermined The underdetermined case is the mst demanding, but als the mst imprtant fr music! Music is (still) mstly in stere, with usually mre than 2 instruments Overdetermined and determined situtatins are nly f interest fr arrays f sensrs r arrays f micrphnes (lcalizatin, tracking) Alternative interpretatin f the linear mdel as a linear transfrm frm signal space t mixture space, with A the transfrmatin matrix and the clumns f A the transfrmatin bases. Juan Jsé Burred. Musical Surce Separatin. 11

12 1. Intrductin Presentatin verview Paradigms, tasks, applicatins Mixing mdels 2. Slving the linear mixing mdel Jint and staged separatin 3. Estimatin f the mixing matrix The need fr sparsity Independent Cmpnent Analysis Clustering methds, ther methds 4. Estimatin f the surces Nrm minimizatin Time-frequency masking 5. Methds using advanced surce mdels Adaptive basis decmpsitin methds Sinusidal methds Supervised methds 6. Cnclusins Juan Jsé Burred. Musical Surce Separatin. 12

13 Slving the linear mdel Direct way t tackle the prblem: Mean Square Errr (MSE) minimizatin: F is the Frbenius nrm ( matrix energy ) BUT: this has infinitely many slutins One must assume prbability distributins fr the invlved variables Maximum A Psteriri (MAP) apprach: maximize Applying Bayes therem and Assuming A has a unifrm distributin (all surce psitins are equally equal) and Assuming the surces are statistically independent this finally yields is the nise variance (if any) and is the assumed lg-density f the surces Juan Jsé Burred. Musical Surce Separatin. 13

Staged separatin Hwever, such a jint estimatin f A and S is: Extremely cmputatinally demanding Unstable with respect t cnvergence Mst methds fllw thus a staged apprach: first estimate the mixing

14 Staged separatin Hwever, such a jint estimatin f A and S is: Extremely cmputatinally demanding Unstable with respect t cnvergence Mst methds fllw thus a staged apprach: first estimate the mixing matrix, then estimate the surces. Nte that, if A is square (determined surce separatin) and invertible (virtually always fr usual mixtures), then the surces can be readily btained by (^ dentes estimatin) In that case, surce separatin amunts t mixing matrix estimatin! In the underdetermined case, A is rectangular and thus nn-invertible. Thus, a secnd surce estimatin stage is needed! Juan Jsé Burred. Musical Surce Separatin. 14

15 1. Intrductin Presentatin verview Paradigms, tasks, applicatins Mixing mdels 2. Slving the linear mixing mdel Jint and staged separatin 3. Estimatin f the mixing matrix The need fr sparsity Independent Cmpnent Analysis Clustering methds, ther methds 4. Estimatin f the surces Nrm minimizatin Time-frequency masking 5. Methds using advanced surce mdels Adaptive basis decmpsitin methds Sinusidal methds Supervised methds 6. Cnclusins Juan Jsé Burred. Musical Surce Separatin. 15

16 Mixing matrix estimatin Simple examples can be visualized by means f scatter plts Determined mixture (2 channels, 2 surces) Underdetermined mixture (2 channels, 3 surces) The crdinates f each data pint are the values f a certain signal cefficient (time sample, time-frequency bin) in each f the mixtures. Data pints tend t cncentrate arund the vectrs defined by the clumns f the mixing matrix: the mixing directins. The gal f mixing matrix estimatin is thus t find such vectrs. Juan Jsé Burred. Musical Surce Separatin. 16

17 The need fr sparsity A signal is said t be sparse if mst f its cefficients (in sme dmain) are zer r clse t zer. Sparse signals will have a peaked prbability distributin. Example: Laplacian signals are sparser than Gaussian signals Laplace distributin: Gemetrical perspective: The sparser the signals, the mre their cefficients will be cncentrated arund the mixing directins, and the easier will be the detectin f the directins. Analytical perspective: Remember the MAP prblem: Measures f sparsity L1-nrm Kurtsis Negentrpy L1-nrm: Penalty fr sparsity Juan Jsé Burred. Musical Surce Separatin. 17

Wavelet Transfrm (DWT) Auditry reslutin frnt-ends Bark ERB (Equal Rectangular Bandwidth) Mel ERB

18 Hw t increase sparsity Time-frequency dmain much sparser than time dmain Spectrgram ( STFT ) Shrt Time Furier Transfrm (STFT) Lgarithmic reslutin frnt-ends Cnstant-Q Transfrm (CQT) Discrete Wavelet Transfrm (DWT) Auditry reslutin frnt-ends Bark ERB (Equal Rectangular Bandwidth) Mel ERB Adaptive signal decmpsitins Basis Pursuit Matching Pursuit Juan Jsé Burred. Musical Surce Separatin. 18

19 Independent Cmpnent Analysis (1) ICA tries t find the mixing directins by aligning the cefficient clusters t the (rthgnal) scatter axes. PCA Whitening ICA Nte that Principal Cmpnent Analysis (PCA), which finds the directins f greatest variance, is nt enugh fr the alignment. Hwever, PCA is used as a first step fr ICA because, when fllwed by whitening (variance nrmalizatin), it makes the mixing directins rthgnal, and thus ICA reduces t finding the remaining rtatin. Als, nte that this is nly pssible fr determined mixtures nt very useful fr music! Axis alignment crrespnds t the surces being statistically independent. Juan Jsé Burred. Musical Surce Separatin. 19

20 Independent Cmpnent Analysis (II) ICA wrks by maximizing sme bjective measure f statistical independence between candidate surces. Methds based n maximizing nngaussianity f the surces FastICA based n kurtsis r negentrpy Methds based n minimizing mutual infrmatin between surces Methds based n Maximum Likelihd (ML) estimatin Bell-Sejnwski (BS) algrithm Natural gradient algrithm FastICA based n ML Tensrial methds ( decrrelate higher rder statistics) FOBI (Furth-Order Blind Identificatin) JADE (Jint Apprximate Diagnalizatin f Eigenmatrices) Hyvärinen + Karhunen + Oja Sund examples (Hyvärinen et al.) Original surces Mixtures Separated surces Juan Jsé Burred. Musical Surce Separatin. 20

Clustering methds Explre the mixture space t find the clusters.

Example: kernel-based angular clustering [Bfill&Zibulevsky01] Kind f smthed histgram

fuzzy C-means clustering... [Bfill&Zibulevsky01] P. Bfill and M. Zibulevsky.

21 Clustering methds Explre the mixture space t find the clusters. Allw underdetermined separatin! Direct inspectin f the scatter plt: sparsity is crucial! Example: kernel-based angular clustering [Bfill&Zibulevsky01] Kind f smthed histgram Mixture scatter and fund directins Estimated density (plar) Als: methds based n k-means, fuzzy C-means clustering... [Bfill&Zibulevsky01] P. Bfill and M. Zibulevsky. Underdetermined Blind Surce Separatin Using Sparse Representatins. Signal Prcessing, Vl. 81, Juan Jsé Burred. Musical Surce Separatin. 21

22 Other methds fr mixing matrix estimatin Phase cancellatin methds ADRess (Azimuth Discriminatin and Resynthesis) [Barry04] Artificial stere panning retains phase and nly changes amplitude between channels phase cancellatin in the interchannel difference spectrgram Methds frm image prcessing applied t the scatter plts (Fig. frm [Barry04]) Example: applicatin f the Hugh transfrm t detect straight lines created by the directin clusters [Lin97] [Barry04] [Lin97] D. Barry, B. Lawlr and E. Cyle. Sund Surce Separatin: Azimuth Discriminatin and Resynthesis. Prc. Int. Cnf. n Digital Audi Effects (DAFX), Naples, Italy, J. K. Lin, D. G. Grier and J. D. Cwan. Feature Extractin Apprach t Blind Surce Separatin. Prc. IEEE Wrkshp n Neural Netwrks fr Signal Prcessing (NNSP), Juan Jsé Burred. Musical Surce Separatin. 22

23 1. Intrductin Presentatin verview Paradigms, tasks, applicatins Mixing mdels 2. Slving the linear mixing mdel Jint and staged separatin 3. Estimatin f the mixing matrix The need fr sparsity Independent Cmpnent Analysis Clustering methds, ther methds 4. Estimatin f the surces Nrm minimizatin Time-frequency masking 5. Methds using advanced surce mdels Adaptive basis decmpsitin methds Sinusidal methds Supervised methds 6. Cnclusins Juan Jsé Burred. Musical Surce Separatin. 23

Surce estimatin by nrm minimizatin In the underdetermined case, A is rectangular and thus nn-invertible. Thus, a secnd surce estimatin stage is needed!

24 Surce estimatin by nrm minimizatin In the underdetermined case, A is rectangular and thus nn-invertible. Thus, a secnd surce estimatin stage is needed! Nrm minimizatin methds Recall (again) the minimizatin prblem Assuming n nise, knwn A and Laplacian (sparse) surces, this simplifies t an L1-nrm minimizatin prblem: A realizatin theref is the shrtest-path algrithm Sund examples fr angular kernel clustering plus shrtest-path estimatin: Independent meldies Musical perfrmance Original surces Mixtures Separated surces Juan Jsé Burred. Musical Surce Separatin. 24

Time-frequency masking (1) Gal: find a mask M that retrieves ne surce when used t filter a

º is the Hadamard (element-wise) prduct Adaptive Wiener filtering Binary time-frequency

Interchannel Intensity (IID) and Phase (IPD) Differences Binary Mask created by selecting

frm [Vincent06]) (Fig. frm [Yilmaz&Rickard04]) [Yilmaz&Rickard04] Ö. Yilmaz and S. Rickard.

25 Time-frequency masking (1) Gal: find a mask M that retrieves ne surce when used t filter a given time-frequency representatin. º is the Hadamard (element-wise) prduct Adaptive Wiener filtering Binary time-frequency masking DUET (Degenerate Unmixing Estimatin Technique) [Yilmaz&Rickard04] Histgram f Interchannel Intensity (IID) and Phase (IPD) Differences Binary Mask created by selecting bins arund histgram peaks. Drawback f t-f masking: musical nise r burbling artifacts (Fig. frm [Vincent06]) (Fig. frm [Yilmaz&Rickard04]) [Yilmaz&Rickard04] Ö. Yilmaz and S. Rickard. Blind Separatin f Speech Mixtures via Time-Frequency Masking. IEEE Trans. n Signal Prcessing. Vl. 52(7), July 2004 Juan Jsé Burred. Musical Surce Separatin. 25

Time-frequency masking (2) Human-assisted time-frequency masking [Vinyes06] Human-assisted selectin f the time-frequency bins ut f the DUETlike histgram fr creating the unmixing mask Implementatin as

26 Time-frequency masking (2) Human-assisted time-frequency masking [Vinyes06] Human-assisted selectin f the time-frequency bins ut f the DUETlike histgram fr creating the unmixing mask Implementatin as a VST plugin ( Audi Scanner ) [Vinyes06] M. Vinyes, J. Bnada and A. Lscs. Demixing Cmmercial Music Prductins via Human-Assisted Time-Frequency Masking. 120th AES cnventin, Paris, France, Juan Jsé Burred. Musical Surce Separatin. 26

27 1. Intrductin Presentatin verview Paradigms, tasks, applicatins Mixing mdels 2. Slving the linear mixing mdel Jint and staged separatin 3. Estimatin f the mixing matrix The need fr sparsity Independent Cmpnent Analysis Clustering methds, ther methds 4. Estimatin f the surces Nrm minimizatin Time-frequency masking 5. Methds using advanced surce mdels Adaptive basis decmpsitin methds Sinusidal methds Supervised methds 6. Cnclusins Juan Jsé Burred. Musical Surce Separatin. 27

28 Advanced surce mdels methds Until nw: blind appraches (nly general, statistical assumptins) The use f (smetimes music-specific) advanced surce mdels allw t imprve separatin quality and t handle highly underdetermined situatins (e.g. separatin frm mn mixtures) Classificatin accrding t a priri knwledge Supervised Based n training the mdel with a sund example database Better quality and mre demanding situatins at the cst f less generality Unsupervised Classificatin accrding t mdel type Adaptive basis decmpsitins (ISA, NMF, NSC) Sinusidal Mdeling Classificatin accrding t mixture type Mnaural systems Hybrid systems cmbining advanced surce mdels with spatial diversity Juan Jsé Burred. Musical Surce Separatin. 28

Independent Subspace Analysis Applicatin f ISA t audi: Casey and Westner, 2000. Applicatin f ICA t the spectgram f a mn mixture.

29 Independent Subspace Analysis Applicatin f ISA t audi: Casey and Westner, Applicatin f ICA t the spectgram f a mn mixture. Each independent cmpnent crrespnds t an independent subspace f the spectrgram. Cmpnent-t-surce clustering (Fig. frm [Casey&Westner00]) The extracted cmpnents usually d nt directly crrespnd t the surces. They must be clustered tgether accrding t sme similarity criterin. Casey&Westner use a matrix f Kullback-Leibler divergences called the ixegram. [Casey&Westner00] Juan Jsé Burred. M. Casey and A. Westner. Separatin f Mixed Audi Surces by Independent Subspace Analysis. Prc, Int. Cmputer Music Cnference (ICMC), Berlin, Germany, Musical Surce Separatin. 29

30 Nnnegative Matrix Factrizatin Matrix factrizatin ( ) impsing nn-negativity. Needed when using magnitude r pwer spectrgrams. NMF des nt aim at statistical independence, but: It has been prven that, under sme cnditins, nn-negativity is sufficient fr separatin. NMF yields cmpnents that very clsely crrespnd t the surces. T date, there is n exact theretical explanatin why is that s! Use fr transcriptin: P. Smaragdis and J.C. Brwn. Nn-Negative Matrix Factrizatin fr Plyphnic Music Transcriptin. Prc. IEEE Wrkshp n Applicatins f Signal Prcessing t Audi and Acustics (WASPAA), New Paltz, USA, Use fr separatin: B. Wang and M. D. Plumbley. Musical Audi Stream Separatin by Nn-Negative Matrix Factrizatin. Prc. UK Digital Music Research Netwrk (DMRN) Summer Cnf., Juan Jsé Burred. Musical Surce Separatin. 30

Nnnegative Sparse Cding Cmbinatin f nn-negativity and sparsity cnstraints in the factrizatin. [Virtanen03]: NSC is ptimized with an additinal criterin f tempral cntinuity.

31 Nnnegative Sparse Cding Cmbinatin f nn-negativity and sparsity cnstraints in the factrizatin. [Virtanen03]: NSC is ptimized with an additinal criterin f tempral cntinuity. Measured by the abslute value f the verall amplitude difference between cnsecutive frames. Mixture Cmpnent 1 Cmpnent 2 [Virtanen04]: Cnvlutive Sparse Cding Imprved tempral accuracy by mdeling the surces as the cnvlutin f spectrgrams with a vectr f nsets. Mixture Cmpnent 1 Cmpnent 2 [Virtanen03] [Virtanen04] T. Virtanen. Sund Surce Separatin Using Sparse Cding with Tempral Cntinuity Objective. Prc. Int. Cmputer Music Cnference (ICMC), Singapre, T. Virtanen. Separatin f Sund Surces by Cnvlutive Sparse Cding. Prc. ISCA Tutrial and Research Wrkshp n Statistical and Perceptual Audi Prcessing (SAPA), Jeju, Krea, Juan Jsé Burred. Musical Surce Separatin. 31

32 Sinusidal Methds Sinusidal Mdeling: detectin and tracking f the sinusidal partial peaks n the spectrgram. Based n Auditry Scene Analysis (ASA) cues f gd-cntinuatin, cmmn fate and smthness f sinusidal tracks. Overall, very gd reductin f interfering surces, but mderate timbral quality. Apprpriate fr Significance-Oriented applicatins (Fig. frm [Every06]) [Virtanen&Klapuri02]: mdel f spectral smthness f harmnic sunds Based n basis decmpsitin f harmnic structures Additive resynthesis f partial parameters Mixture [Every&Szymanski06] Separated surces Spectral subtractin instead f additive resynthesis [Virtanen&Klapuri02] [Every&Szymanski06] Juan Jsé Burred. T. Virtanen and A. Klapuri. Separatin f Harmnic Sunds Using Linear Mdels fr the Overtne Series. Prc. IEEE Int. Cnf. n Acustics, Speech and Signal Prcessing (ICASSP), Orland, USA, M. R. Every and J. E. Szymanski. Separatin f Synchrnus Pitched Ntes by Spectral Filtering f Harmnics. IEEE Trans. n Audi, Speech and Signal Prcessing. Vl. 14(5), Musical Surce Separatin. 32

Supervised Methds (1) Use f a training database t create a set f surce mdels, each ne mdeling a specific instrument. Better separatin as a trade-ff fr generality.

33 Supervised Methds (1) Use f a training database t create a set f surce mdels, each ne mdeling a specific instrument. Better separatin as a trade-ff fr generality. Supervised sinusidal methds [Burred&Sikra07] The surce mdels are cmpact descriptins f the spectral envelpe and its tempral evlutin. The detailed tempral evlutin allws t ignre harmnicity cnstraints, and thus separatin f chrds and inharmnic sunds is pssible. Separatin f chrds Inharmnic separatin Mixture Separated surces Mixture Separated surces [Burred&Sikra07] Juan Jsé Burred. J.J. Burred and T. Sikra. Mnaural Surce Separatin frm Musical Mixtures Based n Time-Frequency Timbre Mdels. Prc. Int. Cnf. n Music Infrmatin Retrieval (ISMIR), Vienna, Austria, September Musical Surce Separatin. 33

34 Bayesian Netwrks Supervised Methds (2) [Vincent06] Multilayered mdel describing nte prbabilities (state layer), spectral decmpsitin (surce layer) and spatial infrmatin (mixture layer). Trained n a database f islated ntes. Allws separatin f sunds with reverb. Learnt prirs fr Wiener-based separatin Mixture Separated surces [Ozerv05] Single-channel HMM mdels f singing vice and accmpaniment. Mixture Separated surces [Vincent06] [Ozerv05] E. Vincent. Musical Surce Separatin Using Time-Frequency Surce Prirs. IEEE Trans. n Audi, Speech and Language Prcessing, Vl. 14 (1), A. Ozerv, O. Philippe, R. Gribnval and F. Bimbt. One Micrphne Singing Vice Separatin Using Surce-Adapted Mdels. Prc. IEEE Wrkshp n Applicatins f Signal Prcessing t Audi and Acustics (WASPAA), New Paltz, USA, Juan Jsé Burred. Musical Surce Separatin. 34

35 Cnclusins Still far frm fully-general, audi-quality-riented system. Mre realistic: significance riented Separatin gd enugh t facilitate cntent analysis Methds based n adaptive mdels, time-frequency masking: Mre realistic mixtures, but mre artifacts and interferences Methds based n sinusidal mdeling: Mre artificial timbre, but less interferences. Current plyphny limitatins: Mn signals: up t 3, 4 instruments Stere signals: up t 5, 6 instruments Juan Jsé Burred. Musical Surce Separatin. 35

36 Literature Very few verview materials n Musical Surce Separatin P. D. O Grady, B. A. Pearlmutter and S. T. Rickard. Survey f sparse and nn-sparse methds in surce separatin. Internatinal Jurnal f Imaging Systems and Technlgy, 15(1) E. Vincent, M. G. Jafari, S. A. Abdallah, M. D. Plumbley and M. E. Davies. Mdel-based audi surce separatin. Technical Reprt C4DM-TR , Queen Mary University, Lndn, UK, T. Virtanen. Unsupervised Learning Methds fr Surce Separatin in Mnaural Music Signals. Chapter in A. Klapuri, M. Davy (Eds.), Signal Prcessing Methds fr Music Transcriptin, Springer Stere Audi Surce Separatin Evaluatin Campaign: Juan Jsé Burred. Musical Surce Separatin. 36

On the use of statistical tools for speech and musical audio processing

On the use of statistical tools for speech and musical audio processing On the use f statistical tls fr speech and musical audi prcessing Mathieu Lagrange Analyse / Synthèse Team, IRCAM Mathieu.lagrange@ircam.fr ATIAM Outline 1. Intrductin 1. Cntext and challenges 2. Past