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Blind source separation using kurtosis, negentropy and maximum likelihood functions

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Abstract

Independent component analysis (ICA) is a thriving tool in separating blind sources from its determined or over-determined instantaneous mixture signals. FastICA is one of the successful algorithms in ICA. The objective of this paper is to examine various contrast functions using FastICA algorithm, and to find highly performed available contrast function for the application of speech signal analysis in noisy environments. The contrast function is a non-linear function used to measure the independence of the estimated sources from the observed mixture signals in FastICA algorithm. Kurtosis, negentropy and maximum likelihood functions are used as contrast functions in FastICA algorithm. The FastICA algorithm using these contrast functions is tested on the synthetic instantaneous mixtures and real time recorded mixture signals. We evaluate the performance of the contrast functions based on signal to distortion ratio, signal to artifact ratio, signal to interference ratio and computational complexity. The result shows the maximum likelihood function performs better than the other contrast functions in noisy environments.

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Abbreviations

BSE:

Blind source extraction

BSS:

Blind source separation

EVD:

Eigen value decomposition

FA:

Factor analysis

FFT:

Fast Fourier transform;

fMRI:

Functional magnetic resonance imaging

HSS:

Heart sound signals

ICA:

Independent component analysis

LSS:

Lung sound signals

NMF:

Non-negative matrix factorization

PCA:

Principal component analysis

SAR:

Signal to artifact ratio

SCA:

Sparse component analysis

SDR:

Signal to distortion ratio

SIR:

Signal to interference ratio

SNR:

Signal to noise ratio

TFR:

Time-frequency representation

References

  • Acharya, D. P., & Panda, G. (2014). A Review of independent component analysis techniques and their applications. IETE Technical Review, 25(6), 320–332.

    Article  Google Scholar 

  • Amari, S., & Cichocki, A. (1998). Adaptive blind signal processing—Neural network approaches. Proceedings of IEEE, 86(10), 2026–2048.

    Article  Google Scholar 

  • Araki, S., Nesta, F., Vincent, E., Koldovsky, Z., Nolte, G., Ziehe, A., & Benichoux, A. (2012). The 2011 signal separation evaluation campaign (SiSec2011): Audio source separation. In Proceedings of international conference on latent variable analysis and signal separation.

  • Araki, S., & Vincent, E. (2019). https://sisec.inria.fr/home/2016-underdetermined-speech-and-music-mixtures/. Accessed 21.

  • Bingham, E., & Hyvarinen, A. (2000). A fast fixed point algorithm for independent component analysis of complex valued signals. International Journal of Neural Systems, 10(1), 1–8.

    Article  Google Scholar 

  • Cardoso, J. F. (1997). Infomax and maximum likelihood for blind source separation. IEEE Signal Processing Letters, 4(4), 112–114.

    Article  Google Scholar 

  • Chiu, S.-H., Lu, C.-P., Wu, D.-C., & Wen, C.-Y. (2008). Geometric transformation based independent component analysis for mixed image separation. Journal of the Chinese Institute of Engineers, 31(3), 497–502.

    Article  Google Scholar 

  • Cichocki, A., & Amari, S. (2002). Adaptive signal and image processing: Learning algorithms and applications. New York: Wiley.

    Book  Google Scholar 

  • Comon, P. (1994a). Tensor diagonalization, a useful tool in signal processing. In Proceedings of IFAC symposium on system identification, Copenhagen, Denmark.

    Article  Google Scholar 

  • Comon, P. (1994b). Independent component analysis, a newconcept? Signal Processing, 36(3), 287–314.

    Article  Google Scholar 

  • Delfosse, N., & Loubaton, P. (1995). Adaptive blind separation of independent sources: A deflation approach. Signal Processing, 45(1), 59–83.

    Article  Google Scholar 

  • Donoho, D. (1980). On minimum entropy deconvolution. In Proceedings of applied time series symposium, Tulsa, Oklahoma.

  • Hyvarinen, A. (1998). New approximations of differential entropy for independent component analysis and projection pursuit. In Proceedings of advances in neural information processing systems, Denver, Colorado, USA.

  • Hyvarinen, A. (1999). Fast and robust fixed point algorithms for independent component analysis. IEEE Transactions on Neural Networks, 10(3), 626–634.

    Article  Google Scholar 

  • Hyvarinen, A., Karhunen, J., & Oja, E. (2001). Independent component analysis, 77. New York: Wiley.

    Book  Google Scholar 

  • Hyvarinen, A., & Oja, E. (1997a). A fast fixed point algorithm for independent component analysis. Neural Computation, 9(7), 1483–1492.

    Article  Google Scholar 

  • Hyvarinen, A., & Oja, E. (1997b). One-unit learning rules for independent component analysis. In Proceedings of advances in neural information processing systems, 9.

  • Hyvarinen, A., & Oja, E. (2000). Independent component analysis: Algorithms and applications. Neural Networks, 13(4–5), 411–430.

    Article  Google Scholar 

  • Khaliq, A. A., Qureshi, I. M., & Shaha, J. A. (2013). Source extraction from functional magnetic resonance imaging data using ICA based on fourth order and exponential contrast functions. Journal of the Chinese Institute of Engineers, 36(6), 730–742.

    Article  Google Scholar 

  • Kumar, M., & Jayanthi, V. E. (2019). Underdetermined blind source separation using CapsNet. Soft Computing,. https://doi.org/10.1007/s00500-019-04430-4.

    Article  Google Scholar 

  • Lacoume, J. L., Gaeta, M. (1990). The general source separation problem. In Proceedings of fifth ASSP workshop on spectrum estimation and Modeling, Rochester, NY, USA.

  • Luo, M., Li, L., Qian, G., & Liao, H. (2015). Blindly detecting the number of signals using HOS in spatially correlated noise. Journal of the Chinese Institute of Engineers, 38(3), 317–321.

    Article  Google Scholar 

  • Meinecke, F. C., Harmeling, S., & Müller, K. R. (2004). Robust ICA for super-Gaussian sources. In C. G. Puntonet & A. Prieto (Eds.), Independent component analysis and blind signal separation., ICA 2004. Lecture notes in computer science, 3195 Berlin: Springer.

    Google Scholar 

  • Nersisson, R., & Noel, M. M. (2016). Heart sound and lung sound separation algorithms: A review. Journal of Medical Engineering & Technology, 41(1), 13–21.

    Article  Google Scholar 

  • Obradovic, D., & Deco, G. (2006). Information maximization and independent component analysis: Is there a difference? Neural Computation, 10(8), 2085–2101.

    Article  Google Scholar 

  • Oja, E., & Kiviluoto, K. (1999). Data analysis, visualization and hidden factor discovery by unsupervised learning. In Proceedings of international joint conference on neural networks, Washington, DC.

  • Pearlmutter, B. A., & Parra, L. C. (1997). Maximum likelihood blind source separation: A context sensitive generalization of ICA. In Proceedings of advances in neural information processing systems, 9.

  • Pham, D. T. (1996). Blind separation of instantaneous mixtures of sources via an independent component analysis. IEEE Transactions on Signal Processing, 44(11), 2768–2779.

    Article  Google Scholar 

  • Pham, D. T., & Garrat, P. (1997). Blind separation of mixture of independent sources through a quasi maximum likelihood approach. IEEE Transaction on Signal Processing, 45(7), 1712–1725.

    Article  Google Scholar 

  • Shalvi, O., & Weinstein, E. (1990). New criteria for blind deconvolution of nonminimum phase systems (channels). IEEE Transaction on Information Theory, 36(2), 312–321.

    Article  Google Scholar 

  • Tong, L., Liu, R-w, Soon, V. C., & Huang, Y.-F. (1991). Indeterminacy and identifiability of blind indentification. IEEE Transaction on Circuits and Systems, 38(5), 499–509.

    Article  Google Scholar 

  • Vincent, E., Gribonval, R., & Fevotte, C. (2006). Performance measurement in blind audio source separation. IEEE Transactions on Audio, speech and Language processing, 14(4), 1462–1469.

    Article  Google Scholar 

  • Wiggins, R. A. (1978). Minimum entropy deconvolution. Geoexploration, 16(1–2), 21–35.

    Article  Google Scholar 

  • Yangi, O., & Jin, J. (2012). Separation of individual operation signals from mixed sensor measurements. IIE Transactions, 44(9), 780–792.

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Chettinad College of Engineering and Technology, NH67, Karur-Trichy Highway, Puliyur, Karur, India

    M. Kumar

  2. PSNA College of Engineering and Technology, Kothandaraman Nagar, Dindigul, India

    V. E. Jayanthi

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  1. M. Kumar
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  2. V. E. Jayanthi
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Contributions

MK and VEJ participated in the design of study. MK carried out the nemrical experiments and drafted the manuscript. All authors read and approved the final manuscript.

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Correspondence to M. Kumar.

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Kumar, M., Jayanthi, V.E. Blind source separation using kurtosis, negentropy and maximum likelihood functions. Int J Speech Technol 23, 13–21 (2020). https://doi.org/10.1007/s10772-019-09664-z

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