blind audio source separation using weight initialized ... - IEEE Xplore

2015 1st International Conference on Next Generation Computing Technologies (NGCT-2015) Dehradun, India, 4-5 September 2015

BLIND AUDIO SOURCE SEPARATION USING WEIGHT INITIALIZED INDEPENDENT COMPONENT ANALYSIS Ritesh Kumar Yadav ∗ Department

∗

Rajesh Mehra ∗ and Naveen Dubey∗

of Electronics and Communication Engineering, NITTR, India,

Abstract—Blind audio source separation is a promising area for various applications like humanoids, human machine interaction or adverse control mechanism, etc. ICA is a predominant approach for source separation in blind scenario. There are various versions of ICA to solve this purpose like Fast ICA, JADE, and C-ICA. The convergence speed and quality of separation is an issue. In this work a weight initialization approach is proposed for optimizing the convergence speed and experimental results reflects up to 28.57% that the proposed weight initialized ICA gives better convergence speed in comparison of Fast ICA. Here a critically determined ideal mixing system is considered where no noise component is taken into account. Keywords: Independent component analysis, Blind source separation, negentropy, kurtosis, Entropy, whitening.

I.

I NTRODUCTION

Independent component analysis (ICA) is a signal processing method which is used for blindly separating the mixtures of signals generated by independent sources. Generally it is required to extract statistically independent components from a set of measured signals. ICA approaches are a fast growing application in various subjects such as speech processing, telecommunication, image enhancement pattern recognition, and biomedical signal processing [1]. In signal processing, independent component analysis (ICA) is an estimation method to separate out a mixed signal into additive subcomponents. There are different ICA approaches, including maximum likelihood estimation and negentropy maximization [2]. Independent component analysis used to decompose a mixed signal into an independent, non-Gaussian signal. The ICA separation of mixed signals gives very good results are based on two assumptions and three effects of mixing source signals. There are two Assumptions: First the source signals are independent of each other and second the values in each source signal have non-Gaussian distributions. Three effects of mixing source signals have first been Independence: As per assumption 1, the source signals are Independent; however, their signal mixtures are not. This is because the signal mixtures share the same source signals. Second is Normality: In terms of Central limit Theorem, every Gaussian signal is consists of a mixture of non Gaussian signals. In a simple way, a sum of two independent random variables usually has a distribution that is closer to Gaussian than any of the two original variables. Here we consider the value of each signal as the random variable. And the third one is Complexity: The temporal complexity of any signal mixture is greater than that of its simplest constituent source signal. The fast ICA algorithm best suitable 978-1-4673-6809-4/15/$31.00 ©2015 IEEE

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to solve this problem. Newton-type is a kind of algorithm used in Fast ICA and the algorithm was based on fixed point algorithm iteration to maximize non-Gaussianity as a measure of statistical independence. Blind audio source separation (BASS) is the problem of extracting unknown source from sensor measurements which are unknown mixtures of the source signal. There are various areas in which the application of BSS used such as speech enhancement, wireless communication [3], image recognition, and biomedical signal processing and image compression [4]. This work proposes a weight initialize approach for fast ICA algorithm which leads fast convergence and good quality of separation in terms of (SIR). The rest of this paper is described as: In section II the theory of ICA and BASS are introduced. Section III describes the convergence of weight initialized approach and algorithm for blind audio source separation. Section IV described the experimental research and techniques to refine the separation of blind audio source. Finally, in section V results show that the improved algorithm employed by us in finding the solution to weaken the sensitivity of the initial value of separation matrix and also enhance the separation effect. II.

THEORY OF BASS AND ICA

The main objective of BASS is to retrieve p audio signal from an assorted audio signal taken by m microphone sensors, can represented mathematically as. [h]Xi n =

p M∑ ij −1 ∑

hij (k)sj (n − k), i = 0..........m,

(1)

(i=0) (i=0)

Where xi (n) is my recorded observed audio signal and Sj (n) is p original audio signal. In blind cases the original signal is unknown. In actual sense, the mixing system is multiple input multiple output linear filter having a source microphone impulse response is higher in each of length Mij [5]. The design of BASS system can also understands by other mathematical model of matrix convolution. The mixing model is given as X =A∗S (2) Whereas the model of un-mixing using BASS ˆ = W (t) ∗ X(t) S(t)

(3)

Where * denotes the matrix convolution, t is the sample index, S (t) = [S1 (t).......SP (t)] it is the vector of p source.


be made which are zero for Gaussian signal and non zero for non-Gaussian signal. Due to this entropy minimization is a leading concern in ICA estimation. A normalized version of entropy gives an appropriate standard for the non - Gaussianity term which is called as Negentropy J. Negentropy is an important measurement for non-gaussianity [10]. This is defined as [h]J(y) = H(ygauss )H(y) (7) Fig. 1.

Where Ygauss is a Gaussian random variable with the same covariance of you. For Gaussian signal negentropy is zero and for non-Gaussian signal, negentropy is maximized.

BASS system design [5]

X(t) = [X(t)...... Xm (t)] it is the detected signal from m microphones [6]. Sˆ (t)= [Sˆ (t)...........Sˆp (t)] it is the response of the retrieved signal. A (t) is the M X P X L mixing array and W (t) is the P X M X L unmixing array. A (t) and W (t) can also be understood as M X P and P X M matrix, where each element is an FIR filter having length L, [5]. To implement a weight initialized ICA for BASS problem certain set of assumption and preprocessing required. A. NON GAUSSIANTY According to the central limit theorem the sum of independent signal with arbitrary distribution tends towards a Gaussian distribution under certain circumstance. Hence Gaussian signal can be taken as a linear combination of a number of independent signals. The independent signal separation can be accomplished by transforming the linear signal as nonGaussian. There is certain commonly used measure of nongaussianty [7]. Kurtosis According to probability theory kurtosis is measured value of peakedness [8]. When data are preconditioned to have unit variance, by the fourth moment of data catharses of signal (x) can be determined. [h]Kurt(z) = Ez23(Ez)2

Before implementing weight initialized ICA algorithms, few preprocessing Steps are carried out.

Focusing It is commonly performed pre-processing step to center the observation vector X by subtracting its mean vector m=E z. The centered observation vector can be interpreted as sticks with [h]Xc = z − m (8) The matrix of mixing remains same after this pre-processing, hence unmixing matrix can be estimated by centering data after the actual estimated can be deduced. Whitening Whitening the observation vector X is a very useful pattern. Whitening involves linearly transforming the observation vector such that its elements are interconnected and have unit variance [11]. The whitening vector satisfies the following relationship [h]Exr xtr = I (9) An easy approach to perform the whitening transformation is to apply eigenvalue decomposition (EVD) of x.

(4)

Where z is a random variable with zero mean. If z is normalized, variance of z is equal to one, i.e. the E [z2 ] = 1. Then (3) is simplified too [h]Kurt(z) = E[z 4 ]3

B. ICA preprocessing

(5)

Entropy Entropy defined in information theory, randomness is the median measure of data carried in each message received. A minimal quantity of mutual information ensures the separation along with non-Gaussianity. Uniformity of the signal corresponds to maximum entropy and entropy is assumed as randomness of a signal [9]. For a continuous valued signal (y), Entropy called as the differential entropy, and is determined as ∫ [h]H(y) = − p(y)logp(y)dy (6) The highest value of entropy represents the Gaussian signal and the spiky nature of the signal is conducted as the lowered value of selective data. In ICA estimated non-Gaussianity must 564

[h]Exxt = V DV t

(10)

Where Exxt is the covariance matrix of x, V is the eigenvector of Exxt and D is the diagonal matrix of eigenvalues. Whitening is a simple and effective procedure that significantly reduces the computational complexity of ICA. III.

WEIGHT INITIALIZED ICA

For BASS with the fast convergence speed we need to implement ICA with weight initialization. The weight initialization method is as follows: consider a system with three observed signals which is mixed source signals and separated out which is original signals. The weight matrix is given as A modified weight initialized approaches is proposed which is described as follows: Proposed weight initialization procedure Step-1: initialize weight matrix randomly. W←rand (n, n) Step-2: calculate mean of matrix Wm . Step-3: update the unmixing matrix


′

W = W - Wm ICA procedure for source separation The FastICA algorithm depends on the choice of nonlinear mapping. First, we choose several different nonlinear functions based on the features of the signals, from which the optimal one will be chosen through the performance index signal to interference ratio (SNR) [12]. The higher SNR is, the better the separation performance will be. The accuracy of execution can be further improved by setting the parameters of the selected optimal function. So the final optimal nonlinear function will be obtained. In decree to overcome this deficiency, the steepest descent method is introduced to obtain an appropriate initial separation matrix. The basic pattern of the steepest descent method is as follows:

1)

Choose an initial orthogonal random matrix W = [w1 , w2 wN ] T and initialize the weight using the proposed Initialization procedure.

2)

Calculate the negative slope of E Xg (WT X)

Fig. 2.

Two source signals.

Fig. 3.

Two mixed signals

Fig. 4.

Signal separated by weight initialized ICA

where ∆E[Xg (WT X)] δw1 = E[xi 2 g, (WT X)] (I = 1, 2. . . . Let W= W -λE [Xg (WT X)] [13] Separate the matrix. To start with, an appropriate initial value can be received through the steepest descent method. Furthermore, Newton iteration is applied to make the final convergence result. The simulation results show that the suggested algorithm is capable to bring down the sensitivity of the initial values, speed up the convergence and avoid the uneven convergence speed. IV.

SIMULATION RESULTS

In order to examine the functioning of proposed algorithms two signals were taken. Signal-1 and signal-2 are records of drum beats of duration 0.3 seconds. Original signals are shown in figure.3 One random 2X2 matrix is used for mixing the signals. The mixed version is shown in figure. 4. Mixed signal applied as input to proposed algorithm. After whitening the mixed signals, both the weight initialized ICA algorithm separates the mixed signals and separated signals are shown in figure.5. Convergence speed of proposed algorithm was 565

compared with Fast ICA for the same data set and The results reflect that The convergence speed gets improved by weight initialization using the proposed method in comparison of FastICA, but The SIR level for Fast ICA is 12.56 dB and 13.2 dB and for proposed algorithm it is 12.68 dB and 12.98dB which is shown in figure.6. Hence there is no significant improvement in SIR.


[2]

[3]

[4]

[5]

[6] Fig. 5.

Convergence speed evaluation

V.

[7]

CONCLUSION

[8]

In this work an approach for unmixing weight initialization is proposed, which gives fast convergence than general Fast ICA approach. The experiment has been performed on two simple signals in critical estimation case and no noise component taken into account. The SIR value of separated signals reflects that there is not a significant difference in SIR value of Fast-ICA and weight initialized ICA. The Proposed algorithm can be hybridized with divergence based ICA, which can give better separation quality.

[9] [10]

[11]

[12]

R EFERENCES [1]

Zhiming Li and Genke Yang, Blind separation of mixed audio signals based on improving Fast ICA, 6th international congress on image and signal processing (CISP-2013), pp. 1638-1642, 2013

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[13]

S.L. Lin and P.C. Tang,application of modified ICA to secure communication in chaotic systems, Lecture notes in computer science, Vol. 4707, pp. 431- 474, 2007. S Kaur, Rajesh Mehra, FPGA implementation of scrambler for wireless communication application, international conference on wireless network and embedded systems, pp.127-129, 2011. Sugreev Kaur, Rajesh Mehra, High speed and area efficient 2D DWT processor based image compression, signal and Image processing: An international journal (SIPIJ), Vol.1, no.2, pp.22-31, December 2010. Naveen Dubey, Rajesh Mehra Blind audio source separation (BASS): An unsupervised approach Int. Journal of Electrical Electronics Engg. Vol. 2, Spl. Issue 1 (2015) e-ISSN: 1694-2310 p-ISSN: 1694-2426, pp. 29-33, 2015. J. V. Stone, 1999. Independent Component Analysis a Tutorial Introduction. The MIT Press, Cambridge, Mass, pp: 193, ISBN: 0262693151. Vicent Emmanuel, Bertin Nancy, G. Remi, Bimbot, Frederic,From Blind to guided audio source separation , IEEE signal processing magazine, pp. 107- 115, May 2014. Ganesh R. Naik, Dinesh Kumar, An overview of Independent component analysis and its application Informatica 35, pp.63-81, 2011. Bhawana Tiwari, Rajesh Mehra,FPGA Implementation of FPGA codac for digital video broadcasting, V-SRD IJEECE, vol.2, pp. 68-77, 2012. A. Hyvrinen, Fast and robust fixed-point algorithms for independent component analysis, Neural Networks, IEEE Transactions on, vol. 10, no. 3, pp. 626, 634, May 1999, doi: 10. 1109/ 72. 761722. Vincent Emmanuel, Bertin Nancy, G. Remi, Bimbot Frederic From Blind to Guided Audio Source Separation, IEEE Signal Processing Magazine, pp. 107-115, May, 2014. U. E. Emir, C. B. Akgl, A. Akin, A. Ertuzun, B. Sankur, and K. Harmanci, Wavelet denoising vs. ICA denoising for functional optical imaging, Neural Engineering, 2003. Conference Proceedings. First International IEEE EMBS Conference on, vol., no., pp. 384, 387, 20-22 March 2003, doi: 10. 1109/ CNE. 2003. 1196841. Ji Ce, Yu Yang, Yu Peng, A new FastICA algorithm of Newton’s iteration, Education Technology and Computer (ICETC), 2010 2nd International Conference on, Vol.3, no., pp. V3-481, V3-484, 22-24 June 2010, doi: 10. 1109/ ICETC. 2010. 5529496