A Block-Based Blind Source Separation Approach With Equilateral Triangular Microphone Array

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1 APSIPA ASC 2011 Xi an A Block-Base Blin Source Separation Approach With Equilateral Triangular Microphone Array Jian Zhang, Zhonghua Fu an Lei Xie Shaanxi Provincial Key Laboratory of Speech an Image Information Processing School of Computer Science, Northwestern Polytechnical University, Xi an, zhangj062464@163.com; mailfzh@nwpu.eu.cn; lxie@nwpu.eu.cn Abstract In this paper we escribe a metho for multiple speech sources separation using an equilateral triangular microphone array. Firstly, the azimuths of horizontal plane are ivie into many units an the spatial features of some irections observe by the microphone array are moele precisely. Seconly, the input mixing signals are segmente into blocks, an then the number of active speakers an their irections are estimate in each block. Thirly, the pre-traine moel with the nearest azimuth to each speaker is aapte to obtain a precise moel, which is then use for time-frequency binary mask estimation. Finally, we separate every source appeare in each block an concatenate those souns from same unit to reprouce the whole stream. The experiments are set up in a real meeting room. The results show that our metho can separate multiple speech sources correctly with low istortion, an are competitive with the total un-blin separation results. Inex Terms: blin source separation, irections of arrival estimation, time-frequency mask, equilateral triangular microphone array I. INTRODUCTION It is known that human has the magical capability of focusing his auitory attention on one talker without being influence by other interferences. The so-calle cocktail party effect remains a challenging problem to machine. The most promising technique to solve this problem might be Blin Source Separation (BSS). There are enormous works have been reporte in the literatures. Generally the BSS approaches can be classe into two types. One is base on Inepenent Component Analysis, which assumes the unerlying sources are inepenent to each other. It works very well only when the suppose mixture moel is correct an generally eals with the over-etermine case [1]. However, this is selom happene in real applications. The other is sparseness-base approach [2,3], which requires that all sources are sparse in Time-Frequency (T-F) omain, an the target is to fin a binary T-F mask for each source. We know that speech signal is sparse in T-F omain. It has been reporte that once the ieal binary mask is obtaine, the speech intelligence can be improve greatly [4]. Multiple speech source separation is important for applications like far-fiel speech recognition, automatic meeting iarization, etc. The major challenge is that the number of active speakers is unknown an may change with time, but most of previous researches assume that the source number is known [2] or un-change [3]. In this paperwe propose a new approach to consier this situation. To cope with omniirectional soun sources, we utilize three microphones to construct an equilateral triangular array. Firstly, we separate the azimuth of horizontal plane into many units an buil Gaussian Mixture Moels (GMMs) for some irections. Seconly, the mixing signals are segmente into blocks. Within each block the inter-microphone time ifference vectors are transforme into incience angles. Then the number of active speakers an their locations are estimate using incience angle histogram. Thirly, the pretraine GMM nearest to each active speaker is aapte to obtain each speaker s precise moel. Finally, a time-frequency binary mask is use to separate each active speech an the signals from same unit are concatenate to reconstruct the whole stream. We examine this approach in a real meeting room, an the experimental results verify that the mixe speech signals can be separate correctly with low istortion an the performance is competitive with the total un-blin metho. The rest of the paper is organize as follows. Section 2 escribes the problem. Section 3 presents our approach. The experiments an the results are shown in Section 4. Section 5 is conclusion. II. PROBLEM DESCRIPTION The triangular array is shown in fig. 1, where the three microphones are locate at the verices of equilateral-triangle. Suppose that sources s 1,...,s N are convolutively mixe an observe by the three sensors as N x i (t) = h ik (l)s k (t l), i = 1, 2, 3 (1) k=1 l Fig. 1. Triangular microphone array.

2 Where h ik (l) represents the impulse response from source k to sensor i. The mixtures x i, i=1, 2, 3 are segmente into P blocks x p i,p=1,...,p. By using short-time Fourier transform (STFT), the mixing moel of each block can be represente in T-F omain as N 1 X p i (f, t) = k=0 H ik (f) S p k (f, t), i = 1, 2, 3 (2) Suppose that, the T-F representations of all source signals are sparse. Then, T-F masking for source separation of each block is performe by S p k (f, t) = M p k (f, t) Xp i (f, t), i = 1 or 2 or 3 (3) { M p 1, S p k (f, t) = k (f, t) is ominant 0, otherwise We separate every source appeare in each block an concatenate those souns from same irection to reprouce the whole stream. Accoringly, the tasks are to correctly estimate the number of active speakers an fin the binary T-F mask for each speaker within every block. III. PROPOSED METHOD Our approach inclues two major steps. In the first step, we estimate the number an the irections of arrival (DOA) of active sources. We suppose the speech signals with the same DOA belong to the same source. In the secon step, the spatial moel for each active source is aapte accoringly an then the separation is performe using the Bayes rule. Finally, the separate source components from all the blocks are concatenate to reconstruct the whole stream. A. The spatial feature Generally, the sparseness-base BSS uses spatial feature to represent the location ifferences of all unerlying sources. The common spatial features contain the inter-microphone amplitue ifference (IAD) an the inter-microphone phase ifferences (IPD). In orer to avoi phase confusing, the istance between the microphones has a limit [5]. We choose 4 cm as the istance in all experiments in this paper. The small istance makes the IAD neglectable. So we only use the IPD feature. In orer to avoi the permutation problem among frequencies, we transfer the IPD feature into time elay. For each T-F point, the IPD can be obtaine as [ ] X p j (f, t) IP D(f, t) = arg, i, j = 1, 2, 3 an i j (5) (f, t) X p i The relation between the time elay δ an the phase ifference is IP D(f, t) = 2πfδ (6) j So, we can obtain the time elay between microphone i an (4) δ ij = 1 2πf arg[xp i (f, t) (7) (f, t)] X p j With three microphones, we compose the three elays to a spatial feature vector as [δ 13 δ 21 δ 32 ]. For every T-F point, we can obtain a feature vector enote as ψ(θ), where the θ means this point belongs to a source with azimuth θ. The relationship between ψ(θ) an θ is use to estimate the source irection. B. To estimate the number an DOAs of active speakers There are a lot of approaches for source localization [6]. Since our aim is to separate the speech mixtures, we must ientify the number of active sources an their irections. We ivie the azimuths of horizontal plane into many equivalent units an estimate the histogram. For the triangular array shown in fig.1, there are three pairs of microphones an each of them has an azimuth ifference of 120. They receive the speech signal s(n) propagating from the irection θ with elevation angle φ. We ignore the φ firstly. The relationship between the azimuth of a single speech source θ an the three elays are escribe by the following equations. δ 13 = c cos(θ 2 π) (8) 3 δ 21 = c cos(θ + 2 π) (9) 3 δ 32 = cos(θ) (10) c Where is the istance of two microphones, c is the soun velocity. We efine a transformation matrix T. to make the x axis of the new coorinate correspons to the ψ(0), an make y axis correspons to the ψ(π) [7]. e1 = ψ(0) = [ c cos( 2 3 π) e2 = ψ( π 2 ) = [ c cos( 1 6 π) Then we transform ψ(θ) as follows T = [ e1 e2 ] T (11) T ψ(θ) = x y = 32 2c 2 c cos( 2 3 π) c ]T (12) c cos( 7 6 π) 0 ]T (13) [ cos(θ) sin(θ) ] (14) Then the irection θ can obtaine by { arc cot( x y ), if(y > 0) θ(f, t) = arc cot( x y ) + π, else (15) The elevation angle will not affect the result because the each component of the elay vector is multiplie by the same factor cos(φ). We ivie the horizontal plane 360 into K equivalent units, so every unit is 360 /K. Then the total energy of every unit is accumulate to buil the histogram as 360(k 1) w(k) = sum(a(f, t) < θ(f, t) 360 k K K ) (16) A(f, t) = 2 X p i (f, t) 2, k = 1,..., K (17) i=1

3 The value of K is etermine accoring to the requirement of the application. The larger K value means the higher accuracy of DOA estimation. But, if K is too large, the error of the source number estimation will increase. In our experiments the K is 36. To eliminate the interferences cause by room reflections, we nee a threshol to select the istinct peaks in the histogram. The tiny peaks might be cause by the fake soun image or the insufficient ata of one source available in the current block. This threshol epens on the value of K an block size, the larger K or block size the larger threshol. In our experiment the threshol is set empirically. The number of peaks that are larger than the threshol can be consiere as the number of active speakers N in this block. Accoringly, the azimuth corresponing to each peak is taken as the DOA of that source. C. The Directional GMMs After the estimation of the number an DOAs of active speakers, the irectional moel for each active source must be built before separation. To avoi the ata insufficient problem, we use moel aaption technique. Specifically, we firstly train some irectional GMMs off-line. Note that the number of GMMs oes not have to match that of active speakers. But if sufficient ata are available beforehan, more irectional GMMs will lea to more precise target irectional moels. Now for each active speaker with known azimuth in current block, the pre-traine GMM with the nearest azimuth is selecte. Suppose the number of active speaker in current block is N, the selecte GMMs are enote as {λ base 1,..., λ base N }. Note that these basic moels o not have to be ifferent. The aaption ata is an important issue. Since the signals observe by the triangular microphones usually contain not only the irect-path signals that are attenuate an elaye replicas of the sources, but also the multi-path reflecte signals. Aitionally, speech signal is not ieal sparse. Hence, sometimes ifferent sources may contribute to the same T-F point. To eliminate these isturbances, it is necessary to fin the reliable T-F points that only one source is ominant an we can use the corresponing features to aaptive the basic source moels. Generally, for each usable peak in the DOA histogram, the T-F point of which the irection is closer is more reliable [8]. Specifically, the T-F point of which the irection θ satisfies the following option is selecte for the k-th source {(f, t) (k 1) < θ(f, t) k K K } (18) If K is too large or the block size is too small, the option can be relaxes as follows {(f, t) (k 2) < θ(f, t) (k + 1) K K } (19) With these reliable T-F points, the corresponing feature vectors are use for aaption. The aaption is implemente by only 2 4 expectation maximum (EM) operations. Then we obtain the precise target irectional moel for each active speaker, enote as {λ tar 1,..., λ tar N }. D. The Separation an the Reconstruction After we obtain every speaker s moel, we can merge the other moels together to make a backgroun moel λ bk for every source. N λ bk i = λ tar j (20) j=1,j i When both the backgroun moel an the target moel are available, the binary mask for each source can be estimate using Bayes rule. The binary mask is simply estimate base on the likelihoo comparison. For each T-F point, the spatial feature of the mixe signal is enote as O(f, t). The binary mask of the source i can be obtaine using M p i (f, t) = { 1, p(λbk i O(f, t)) < p(λ tar i O(f, t)) 0, otherwise (21) Then the separation is performe use (2). The speech signal of the source i can be reconstructe using Inverse short time Fourier transform (ISTFT) an overlap-aing metho. The stream concatenation is simple here. We suppose the speech signals with the same unit belong to the same source. Hence the whole speech stream s j, j = 1,..., N are reconstructe by concatenating together all the segments of that source s p j, p = 1,..., P. A. Experiments setup IV. EXPERIMENTS AND DISCUSSIONS The experiments are performe in a real meeting room an the eployment of the microphones an louspeakers is shown in Fig.2. A high-fielity louspeaker is place respectively at sixteen points 1.8m aroun of the triangular microphone array. The auio signals playe through the louspeaker are some clean speech. These auio signals are playe with the same average soun level an then mixe in computer. Louspeaker (120cm height, high-fielity) Microphone (120cm height, omni-irectional) Room Size: 6.5m(W)*4.6m(L)*3.3m(H) Reverberation time: 160ms Groun Noise: 25B Fig. 2. Experiment setup. We use the interference reuction ratio (IRR) an loglikelihoo ratio (LLR)[9] to measure the interference reuction

4 an the speech istortion respectively. 2 Yi (f, t) (1 M (f, t)) IRR = f,t Yi (f, t) f,t { LLR = E log ( 2 αp Rc αpt αc Rc αct The corresponing DOA histogram is show in fig.5. It is very clear four peaks are istinct on the correct azimuth angles. 100% (22) )} (23) Where Yi (f, t) is the pure interference; M (f, t) is the binary mask obtaine using (18); αp is the LPC vector of the separate speech; αc is that of the original clean speech an Rc is the autocorrelation matrix of the original clean speech signal; E{} is the expectation function. For comparison, the un-blin results an the ieal binary mask results are also shown. Un-blin means the location of every source is known, an its moel, i.e. the GMM, is traine well separately in avance. The ieal binary mask (IBM) is the upper boun of the separation performance. It is create using knowlege of the signals before they were mixe. Mieal (i) = S i (f, t) > Yi (f, t), i = 1,..., N Fig. 5. result of DOA. The separation results of our metho are shown in fig.6. The results of un-blin separation are show in fig.7 an the IBM results are shown in fig.8. (24) Where Si (f, t) is the STFT of the esire signal. We mix six sources, an their angles are {30, 90, 150, 210, 270, 330 }. We also select eight irectional moels as the basic moels. Their angles are {0, 45, 90, 135, 180, 225, 270, 315 }. The block length is 5 secons, an within each block, 2 6 speech sources as ranom selecte an mixe. Totally, we simulate 120 blocks with 10 minutes of mixe ata. The 360 of horizontal plane is ivie to 36 units, so every unit is 10. Fig.3 an Fig.4 show an example of one block. There are four active sources an their angles are 30, 150, 210 an 330, respectively. Fig.3 shows the original sources an fig.4 shows the mixe observations. Fig. 6. Separation results of our approach. IRR {0.8580, , , }; LLR {0.5714,0.6255, , } Fig. 7. Separation results of un-blin approach. NRR-U {0.9395, , , }; LLR-U {0.5689, , , } Fig. 3. original signals. Fig. 8. Separation results of IBM. IRR-I {0.9749, , , }; LLR-I {0.3950, , , } Fig. 4. mixe signals. The quantitative results are liste in Table I. Note that the higher the IRR is, the more interference is eliminate, an the lower the LLR is, the smaller istortion the speech has.

5 TABLE I EXPERIMENT RESULTS source LLR LLR-U LLR-I IRR IRR-U IRR-I T-len.(min) [7] M. Yoshia, D. Ning an N. Hamaa, Blin Speech Separation by Integrating Three Pairs of Phase Differences of Equilateral Triangular Microphone Array, 2010 International Symposium on Intelligent Signal Processing an Communication Systems (ISPACS 2010), [8] Y. Lv an S.T. Li, Uneretermine Blin Source Separation of Anechoic Speech Mixtures, 9th International Conference on Signal Processing, 2008 (ICSP 2008), [9] Y. Hu an P. C. Loizou, Evaluation of objective quality measures for speech enhancement, IEEE Trans. Auio, Speech, an Language Process., vol. 16(1), pp , T-Len means the total length of speech. Accoring to the experimental results, the IBM achieves the best performance, an our approach has the competitive performance with the total un-blin separation approach, an both are close to the IBM performance. Almost 90% interferences are eliminate. The results show that our approach can separate the mixtures correctly with low speech istortion without knowing the number an DOAs of the active sources. V. CONCLUSION This paper introuces a block-base approach for the uneretermine blin source separation using binary T-F masks. The main iea is to moel each soun source. Firstly, we estimate the source number an their irections. An select reliable T-F points for each source. Seconly, we loa moel for every source an use these reliable T-F points to aapt the moel. Than we calculate binary mask accoring these moels. The last step, the separate source components from all the blocks are concatenate to reconstruct the whole signal. The experimental results show the effectiveness. ACKNOWLEDGMENT This work was supporte in part by the National Natural Science Founation of China ( ), Aeronautical Science Founation of China ( ) an Doctoral Program of Higher Eucation in China ( ). This work was also supporte By grauate starting see fun of Northwestern Polytechnical University (Z ). REFERENCES [1] Ricaro Vigario An Erkki Oja, BSS an ICA in Neuroinformatics: From Current Practices to Open Challenges. IEEE Reviews in Biomeical Engineering, vol 1: pp , [2] C. Hummersone, R. Mason an T. Brookes, Ieal Binary Mask Ratio: A Novel Metric for Assessing Binary-Mask-Base Soun Source Separation Algorithms. IEEE Transactions on Auio, Speech, an Language Processing, in press. [3] S. Araki, H. Sawaa, R. Mukai an S. Makino, Uneretermine blin sparse source separation for arbitrarily arrange multiple sensors, Signal Processing, vol. 87(8): pp , [4] S. Araki, T. Nakatani, H. Sawaa an S. Makino, Blin Sparse Source Separation For Unknown Number of Sources Using Gaussian Mixture Moel Fitting With Dirichlet Prior, IEEE International Conference on Acoustics, Speech an Signal Processing, 2009 ( ICASSP 2009) [5] Z.H. Fu, L. Xie an D.M. Jiang, Dual-microphone noise reuction base on semi-blin DUET, International Symposium on Chinese Spoken Language Processing (ISCSLP), [6] M. Swartling, B. Säberg, N. Grbic, Source localization for multiple speech sources using low complexity non-parametric source separation an clustering, Signal Processing, vol. 91 (8), pp , 2011.