Multiple Sparse Sources Separation Based on Multichannel Frequency Domain Adaptive Filtering

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APSIPA ASC 011 i a Multiple Sparse Sources Separatio Based o Multichael Frequecy Domai Adaptive Filterig iaoyu CHEN, Zhog-hua FU ad Lei IE Shaaxi Provicial Key Laboratory of Speech ad Image Iformatio

c Abstract Uderdetermied sparse sources separatio is a challege problem especially i adverse eviromet, where there are ofte some o-sparse iterfereces or more tha oe sparse iterfereces located closely

1 APSIPA ASC 011 i a Multiple Sparse Sources Separatio Based o Multichael Frequecy Domai Adaptive Filterig iaoyu CHEN, Zhog-hua FU ad Lei IE Shaaxi Provicial Key Laboratory of Speech ad Image Iformatio Processig, Northwester Polytechical Uiversity, i a cxy313186@gmail.com, {mailfzh, lxie}@wpu.edu.c Abstract Uderdetermied sparse sources separatio is a challege problem especially i adverse eviromet, where there are ofte some o-sparse iterfereces or more tha oe sparse iterfereces located closely to the target sources. While i some applicatios, such as i-car or hads-free eviromets, refereces of the iterfereces (P ) comig from loudspeakers are available. Commo sparse source separatio approaches have ot yet used these referece iformatio, we call them traditioal approaches i this paper. We propose a FD-MENUET (Frequecy domai adaptive filterig based Multiple sensor degeerate Umixig Estimatio Techique) approach, i which we get full use of those referece iformatio to help to separate the target sources. Eve if o referece is available, the approach would oly degeerate to the traditioal approaches. The experimetal results show that the proposed approach is more geeral ad could achieves better separatio performace tha the traditioal oe. I. INTRODUCTION Uderdetermied Sparse Source Separatio is more iterestig i recet years for its capability of hadlig the problem that the umber of sources N could be bigger tha the umber of sesors M (N > M). For the advatage of beig implemeted i real time, the biary mask approaches such as Degeerate Umixig Estimatio Techique (DUET) 1] ad Multiple Sesor DUET (MENUET) ] are more attractive i all approaches. It assumes that the sources are efficietly sparse, ad assigs the mask with 1 if the eergy at a timefrequecy (T-F) uit is cosidered as beig from the target, ad 0 otherwise. While the ideal biary mask (IBM) approach sets the mask 1 if the target source s eergy exceeds other sources ad 0 otherwise 3]. However, i practice, there are ofte iterfereces that may be o-sparse or locate closely to the target source, ad the refereces are usually available whe these iterfereces come from loudspeakers. I such situatio, we could o loger assume that at most oe source is domiat at each T-F uit. The, the traditioal approach without usig these refereces would be difficult or eve impossible to separate the target sources. So for the problems, our motivatio is that usig adaptive filterig techique to cacel these iterfereces compoets from the T-F uits i frequecy domai before features extractio. Adaptive filterig techiques have bee developed from time domai to frequecy domai ad sigle chael to multichael. Most adaptive algorithms i time domai could be classified ito Least Mea Square (LMS) family, Recursive Least Square (RLS) family ad Affie Affie Projectio (AP) family. I recet years frequecy domai adaptive filter (FDAF) become more ad more attractive 4 6], because comparig with algorithms i time-domai it coverges faster, could be effectively applied i multi-chael (MC) case (MC- FDAF) while requirig poor cross correlatio coditios a- mog chaels, ad update step size of the filter coefficiets could be idepedet to each other at differet frequecies 7]. For advatages metioed above, we apply MC-FDAF ito our system. This paper is orgaized as follows. I Sectio II, we itroduce the proposed flow model, defiitios ad problems descriptio. Sectio III describes the procedures of the proposed approach. Experimets setup ad discussios are preseted i Sectio IV. The last sectio cocludes this paper. II. BACKGROUND DESCRIPTION I the paper, lowercase ad uppercase bold fot represet vector ad matrix quatities, respectively; all vectors are colum vector; ad ] T stads for matrix or vector traspositio. Uderlied quatities deote DFT-domai variables ad k is a discrete time idex. A. Model ad Defiitio We cosider the itegratio of all sources ad sesors as a MIMO system with M iput chaels ad Q output chaels. The received sigal from the qth sesor at time k is give by x q (k) = M u T m(k)h mq (k) = u T (k)h q (k) (1) m=1 where M = N + P ad u m (k) = u m (k), u m (k 1),, u m (k L + 1)] T () h mq (k) = h mq,0 (k), h mq,1 (k),, h mq,l 1 (k)] T (3) are a vector cotaiig the latest L samples captured from the mth iput chael ad the curret adaptive filter for the path from source m to sesor q, respectively. There are N orefereced sources ad P refereced sources. For coveiet, we itegrate each of them for all m i oe vector h q (k) = h T 1q(k), h T q(k),..., h T Mq(k)] T (4)

Fig. 1. The proposed model ad flow procedures.

We maily cocer about the situatio that o-refereced sources umber N is greater tha sesors umber Q (N > Q), amely uderdetermied situatio.

The proposed approach aims to separate out each source y q (k) from every mixed sigal x q (k), ad make good use of all valuable iformatio to obtai more pure y q (k). B.

2 Fig. 1. The proposed model ad flow procedures. u(k) = u T 1 (k), u T (k),, u T M(k)] T = s T 1 (k),, s T N (k), r T 1 (k),, r T P (k)] T (5) where s T (k) ad r T p (k) are the th o-refereced source ad the pth refereced source, respectively. We maily cocer about the situatio that o-refereced sources umber N is greater tha sesors umber Q (N > Q), amely uderdetermied situatio. There is o restrictio to the umber of referece sources (P 0), but we focus o the situatio that the umber of referece sources P. The proposed approach aims to separate out each source y q (k) from every mixed sigal x q (k), ad make good use of all valuable iformatio to obtai more pure y q (k). B. Problems Descriptio 1) Problem of traditioal approach: Accordig to the s- parse theory 1, ], we kow each source sparsely distributes i the time-frequecy domai, ad it is a small probability evet that multiple sources appear i the same T-F uit of the mixture. Accordigly, it ca be approximated that the T-F uit likely belogs to the source whose eergy is major here x L,q (f, i) u T L,m(f, i)h L,mq (f, i) (6) where i is a block time idex, L is DFT legth. However, i practice, some sources are ot sparse eough or eve osparse, ot oly the promiet-eergy source but also other cosiderable-eergy sources exist i the same T-F uit. Due to the greatly icreased probability of multiple sources eergy overlap i oe T-F uit, we ca ot approximate it as (6). ) Problem of sesor pair: Iteraural Level Differece (ILD) ad Iteraural Time Differece (ITD) 8] are two importat ad popular features to estimate the biary mask. Whe the locatios of source ad sesor pair follow SF 1 SF = ±a (0 a F 1 F ) (7) where a is a costat scalar, ad SF 1, SF, F 1 F ad a represet the legth from source S to sesor F 1 ad sesor F, the legth betwee F 1 ad F, the distace differece betwee S to F 1 ad F, respectively. The ITD features will be exactly the same, the for omidirectioal sesor pair, it would be difficult to separate the sources. Particularly, whe a = 0, eve directioal sesor pair could ot separate them. 3) Problem of multiple sources earby: I practice, there are ofte some sources located closely to each other, oticed that the positios of these sources ad sesor pair would ot satisfy (7). No matter for omidirectioal or directioal sesor pair, the ILDs ad ITDs of these sources are extremely similar, especially i reverberate eviromet. It is difficult to separate these sources efficietly. I Fig., there are 5 sparse sources i (a) ad (c), i which sources are close to each other. Results shows that there are oly 4 peaks, the sources are mixed ito oe peak. For detail discussio, see IV-B. phase differece phase differece (a) (c) phase differece (b) phase differece (d) Fig.. Example cotours ad s of traditioal ad proposed approaches i the coditio two sources are close to each other with T 60 = 60ms. We chose oe ad the phase differece of each features to plot. (a) ad (c) are traditioal results; (b) ad (d) are proposed results. III. PROPOSED METHOD I order to improve the separatio performace, especially i the challegig situatios metioed above, we propose to make full use of the possible refereces. The mai procedures of our proposed approach are preset i Fig.1. A. Adaptive filterig Procedures Before feature extractio, we process adaptive filterig first wheever oly refereced sources are preset. Here we ca use double talk detector (DTD) 9, 10] as a cotroller to determie whe the adaptive filter should work. Ad we must take differet DFT trasforms before ad after every adaptive

3 filterig iteratio. I adaptive filterig procedure, Lth DFT is employed, for refereced source r p R L LP (i) = R L,1 (i), R L, (i),..., R L,P (i) ] (8) r p (il L) R L,p (i) = diag F L L. (9) r p (il + L 1) where F L L is a L L DFT matrix with elemets e jπvl/l, where v, l = 0,..., L 1; for qth sesor received sigal x q ] 0 L Q (i) = F L Q L L (10) x 1 (i),..., x q (i),..., x Q (i) x q (i) = x q (il), x q (il + 1),..., x q (il + L 1)] (11) ad for frequecy domai adaptive filter H LP Q (i) = h LP,1 (i),..., h LP,q (i),...h LP,Q (i) ] (1) ] h1q (i),..., h h LP,q (i) = F pq (i),...h P q (i) L L 0 L P (13) The MC-FDAF is used 5, 7] to update the adaptive filter util o-refereced sources are preset. E L Q (i) = L Q (i) G 01 (14) L LR L LP (i)h LP Q (i 1) H LP Q (i) =H LP Q (i 1) where G 01 L L, G10 LP LP + G 10 LP LP K(i)E L Q (i) (15) ad the kalma gai K(i) are derived i 5, 11]. We ca also calculate the kalma gai by usig 1]. The all sources are preset ad it is oly eeded to process Lth DFT with F L L similar to F L L, addig a frame widow is optioal here. The iterfereces with refereces ca be elimiated from the mixture by where L Q(i) = L Q (i) P r L,p (i) H L,p (i) (16) p=1 L Q (i) = x L,1 (i),..., x L,q (i),..., x L,Q (i) ] (17) H L,p (i) = h L,p1 (i),..., h L,pq (i),..., h L,pQ (i) ] (18) ad h L,pq (i) is Lth DFT trasform of the curret filter for the path from source p to sesor q. After the adaptive elimiatio, the we could make separatio o L Q(i). B. Separatio Procedures Setp 1. Clusterig: Because a idividual cluster i the correspods to a idividual source 1], we ca separate each source by selectig the observatio sigal at T-F uits i each cluster with a biary mask ]. Suppose we kow the umber of o-refereced sparse sources is N, the by usig the popular clusterig methods such as K-meas or GMM to cluster the features Θ(f, i) extracted from L Q(i), ad we ca obtai N curret clustered ceters C (i), where 1 N. Kids of features are discussed i ]. Step. Patter recogizatio: By extractig ew feature Θ q1 q (f, i) from x L,q 1 (i) ad x L,q (i), we ca use distace or probability as the criterio to determie which clustered ceter, geerated i step 1, the ew feature belogs to. The we could obtai the biary mask accordigly by { 1 Θq1 q M,q1q (f, i) = (f, i) C,q1 q (i) (19) 0 otherwise By applyig the biary mask to x L,q 1 ad x L,q, we ca obtai the th source s compoets from sesor q 1 ad q, respectively y,q 1 (f, i) = M,q1 q (f, i) x L,q 1 (f, i) y,q (f, i) = M,q1 q (f, i) x L,q (f, i) (0) We ca fially obtai the separated sigal y,q (i) from the qth sesor s mixed-sigal x q (k) by usig overlap-add method, 13], y,q (i) = 1 λ λ 1 β=0 y β,q (i β) (1) where λ = L/S is overlap factor, S is frame shift legth, y,q (i) is a vector with legth S, y β,q (j) =y,q((j + β)s + 1), y,q((j + β)s + ),..., y,q((j + β + 1)S)] T () where y,q(v) is the vth elemet of y,q(j), ad y,q(j) is the iverse DFT trasform of y,q (j). A commo problem i usig biary mask is that there are ievitable errors i estimatig the masks, this would lead to musical oise. The problem ca be preveted by usig spectral smoothig techique 14]. IV. EPERIMENTS I this sectio, we show the performace of the proposed approach ad compare it with the traditioal ] ad the IBM approaches. A. Experimet Eviromet The experimets are carried out i a typical-sized room with T 60 = 00ms ad there are oe sesor pair. We obtai the sesor received sigals by covolvig the source sigals ad the related measured impulse resposes. The iter-distace of the sesor pair is 4cm ad samplig frequecy is 8KHz. The sources iclude chiese speech ad white oise. Istead of

microphoe(omi-directioal) room size: 650x460x330 :(33, 100, 170) DTD, we update the adaptive filter first util o-refereced T60: 00ms mic:(37, 100, 170) loudspeaker sources are preset.

4 microphoe(omi-directioal) room size: 650x460x330 :(33, 100, 170) DTD, we update the adaptive filter first util o-refereced T60: 00ms mic:(37, 100, 170) loudspeaker sources are preset. uit: cm :(15, 105, 160) sp: speech The frame size of STFT is L = 51, the frame shift legth :(435, 105, 160) ref1:(75, 190, 175) ref: referece sigal is S = 18 ad the chose feature ] is sp:(35, 180, 170) sp:(345, 185, 170) Vertical Plae Nearby ref:(350, 180, 170) ]] ref:(35, 190, 180) ref(sp) xq1 (f, i) xq (f, i) x (f, i) sp 1 q arg Θq1 q (f, i) =,, sp ref(sp) Aq1 q (f, i) Aq1 q (f, i) αq1 q f xq1 (f, i) where Aq1 q (f, i) = xq1 (f, i) + xq (f, i), αq1 q = (A) (B) mic mic 4c 1 dq1 q is the ormalizatio factor, c = 343 m/s is the speed of soud propagatig i the air ad dq1 q is the distace sp:(35, 180, 170) sp:(35, 180, 170) No-sparse Normal ref:(365, 00, 00) ref:(365, 00, 00) betwee the q1 th sesor ad the q th sesor. We cluster the sp sp extracted features by usig k-meas method. The adaptive filter L ref(sp) ref(white oise) legth is L, the update rate is ω = (1 1/(3L)) ad the frame overlap factor is λ = L/S. We performed 4 group experimets, see Fig.3. There are 5 (C) (D) mic mic sources with 3 o-refereced oes ad refereced oes i every group. I the first group, two sparse sources are both Fig. 3. Experimet eviromets setup. satisfied (7) with a = 0; i the secod group, two sparse sources are located closely; i the third group, there is a osparse source with referece; the last group is the situatio that all sparse sources ca be separated by traditioal approach. We compared the separatio performaces of the approaches usig Sigal to Iterferece Ratio (SIR) ad Sigal to Distortio Ratio (SDR) as the evaluatio measures. k yq (k) SIR =10log10 j k j = yq (k) k xq (k) 10log10 j k j = xq (k) k xq (k) SDR =10log10 k xq (k) βyq (k D) v (k) ad xvq (k), (1 v N ), are the compoets where yq that beloged to sv (k), mixed i yq (k) ad xq (k) respectively; β ad D are used to compesate the amplitude atteuatio v ad the time delay betwee yq (k) ad xvq (k). β = 1 ad D = 0 i our statistics. B. Results Ad Discussio Note that we oly cocer the 3 o-refereced sources ad the results are show i Fig.4 ad Fig.5 i which (A)-(D) are relative to (A)-(D) i Fig.3. Fig.4 is geerated i the situatio (D) of Fig.3. We ca see that the proposed results are more pure tha the traditioal s. The ituitive compariso i the situatio (B) is show i Fig., i which (a) ad (c) are results of traditioal approach, there are 5 sources are preset but oly 4 peaks are distict; (b) ad (d) are geerated by the proposed approach, i the 5 sources, the 3 sources are respect to the 3 distict peaks respectively. I situatio (A), the features of the two sources are exactly the same, the traditioal approach ca ot separate these two sources. The proposed approach cacel the cofused refereced source ad separate other sources well, see Fig.5. Fig. 4. Spectrum of o-refereced sources resulted from traditioal ad proposed approach i the coditio Fig.3 (D). (a): the sesor received sigal s spectrum of each o-refereced sources; (b): the spectrum of the 5 sources mixtures; (c): traditioal approach results; (d): proposed approach results. Results i (B) is similar to (A) ad the features of the two earby sources are similar. I traditioal results, these two separated sources iterfere each other, i worst case, this situatio eve cause to large deviatio of the other 3 cluster s regular ceter. I (C), there is a o-sparse source, white oise with -db, i the mixture. The traditioal approach could still work with small eergy of the o-sparse source, but the separatio results are poor. While heavy eergy will lead to impossible separatio. The proposed approach elimiates the compoets of the o-sparse source ad obtais a good separatio result. (D) is a ormal situatio that the traditioal approach geerally deal with. All sources are sparse ad spatial features are differet from each other. The result shows

5 There are may issues remai such as source umber estimatio, precise DTD ad reverberatio problem, which will be further studied i our future work. ACKNOWLEDGMENT This work was supported i part by the Natioal Natural Sciece Foudatio of Chia ( ), Aeroautical Sciece Foudatio of Chia ( ) ad Doctoral Program of Higher Educatio i Chia ( ). Fig. 5. Average SIR improvemet ad SDR of o-refereced sources i usig traditioal, proposed ad IBM approaches i each coditios (A)-(D) relative to (A)-(D) i Fig.3. that the performace of the proposed approach is also better tha the traditioal oe i this situatio. The results of the IBM approach are preset as well. Note that the IBM results are implemeted without adaptive filterig ad all 5 sources are separated. However, i the proposed approach, oly the 3 o-refereced sources are eeded to be separated. Hece the proposed results are sometimes better tha those of the IBM. The compariso differeces of average SIR ad average SDR i situatio (A)-(D) amog traditioal, proposed ad IBM approaches are listed i Table I. It also shows the proposed approach is better tha the traditioal oe. TABLE I DIFFERENCE OF AVERAGE SIR AND SDR AMONG THE THREE APPROACHES SIRdB] SDRdB] Speech IBM-P a IBM-T b P-T IBM-P IBM-T P-T sp a Proposed approach b Traditioal approach V. CONCLUSIONS We proposed a ovel FD-MENUET (Frequecy domai adaptive filterig based MENUET) approach. It exteds the applicable situatios of the traditioal approach as follows: 1) sparse sources are lived with refereced o-sparse sources; ) some refereced iterferes are close to target sources or follow the relatio (7) with the sesor pair; 3) the situatio that traditioal approach could achieve ad some sources have referece sigals. We derived a geeral MIMO solutio, ad whe there is oe refereced sources, the proposed approach will degeerate to the traditioal oe. Due to the fiite legth of the adaptive filters, the separatio performace is still subject to the coditio of reverberatio. REFERENCES 1] O. ilmaz ad S. Rickard, Blid Separatio of Speech Mixtures via Time-Frequecy Maskig, IEEE Trasactios o Sigal Processig, vol. 5, o. 7, pp , 004. ] S. Araki, H. Sawada, R. Mukai, ad S. Makio, Uderdetermied blid sparse source separatio for arbitrarily arraged multiple sesors, Sigal Processig, vol. 87, o. 8, pp , ]. Li ad D. Wag, O the optimality of ideal biary timefrequecy masks, Speech Commuicatio, vol. 51, o. 3, pp , ] J. Beesty ad D. R. Morga, Frequecy-domai adaptive filterig revisited, geeralizatio to the multi-chael case, ad applicatio to acoustic echo cacellatio, Proc of ICASSP 000, vol., pp. II789 -II79 vol., ] H. Bucher, J. Beesty, ad W. Kellerma, Geeralized multichael frequecy-domai adaptive filterig: efficiet realizatio ad applicatio to hads-free speech commuicatio, Sigal Processig, vol. 85, o. 3, pp , ]. Huag ad J. Beesty, A class of frequecy-domai adaptive approaches to blid multichael idetificatio, IEEE Tras Sigal Processig, vol. 51, o. 1, pp. 11 4, ] W. Herbordt, H. Bucher, S. Nakamura, ad W. Kellerma, Multichael Bi-Wise Robust Frequecy-Domai Adaptive Filterig ad Its Applicatio to Adaptive Beamformig, IEEE Trasactios o Audio, Speech ad Laguage Processig, vol. 15, o. 4, pp , ] J. F. Cullig, M. Hawley, ad R. Litovsky, The role of headiduced iteraural time ad level differeces i the speech receptio threshold for multiple iterferig soud sources, Joural of the Acoustical Society of America, vol. 116, o., pp , ] T. Gäsler ad J. Beesty, The fast ormalized crosscorrelatio double-talk detector, Sigal Processig, vol. 86, o. 6, pp , ] H. Bucher, J. Beesty, T. Gäsler, ad W. Kellerma, Robust Exteded Multidelay Filter ad Double-Talk Detector for Acoustic Echo Cacellatio, IEEE Trasactios O Audio Speech Ad Laguage Processig, vol. 14, o. 5, pp , ] H. Bucher ad W. Kellerma, Improved Kalma gai computatio for multichael frequecy-domai adaptive filterig ad applicatio to acoustic echo cacellatio, IEEE Iteratioal Coferece o Acoustics Speech ad Sigal Processig, vol., o. 1, pp , 00. 1] G. Ezer ad P. Vary, Frequecy-domai adaptive Kalma filter for acoustic echo cotrol i hads-free telephoes, Sigal Processig, vol. 86, pp , Jue ] P. Somme ad J. Jayasighe, O frequecy domai adaptive filters usig the overlap-add method, Circuits ad Systems,IEEE Iteratioal Symposium o, vol. vol.1, pp. 7 30, ] T. Ja, W. Wag, ad D. Wag, A multistage approach to blid separatio of covolutive speech mixtures, Speech Commuicatio, vol. 53, pp , Apr. 011.

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