Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Underdetermined Convoluted Source Reconstruction Using LP and SOCP, and a Neural Approximator of the Optimizer

  • Conference paper
Independent Component Analysis and Blind Signal Separation (ICA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 3889))

Abstract

The middle-term goal of this research project is to be able to recover several sound sources from a binaural life recording, by previously measuring the acoustic response of the room. As a previous step, this paper focuses on the reconstruction of n sources from mconvolutive mixtures when m < n (underdetermined case), assuming the mixing matrix is known.

The reconstruction is done in the frequency domain by assuming that the source components are Laplacian in their real and imaginary parts. By posterior likelihood optimization, this leads to norm 1 minimization subject to the mixing equations, which is an instance of linear programming (LP). Alternatively, the assumption of Laplacianity imposed on the magnitudes leads to second order cone programming (SOCP).

Performance experiments are run from synthetic mixtures based on realistic simulations of each source-microphone impulse response. Two sets of sources are used as benchmarks: four speech utterances and six short violin melodies. Results show S/N reconstruction ratios around 10dB. If any, SOCP performs slightly better.

SOCP is probably too slow for real-time processing. In the last part of this paper we train a neural network to predict the response of the optimizer. Preliminary results show that the approach is feasible but yet inmature.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Olshausen, B.A., Field, D.J.: Sparse coding with an overcomplete basis set: A strategy employed by V1? Vision Research 37, 3311–3325 (1997)

    Article  Google Scholar 

  2. Zibulevsky, M., Pearlmutter, B.A.: Blind Source Separation by Sparse Decomposition. TR No. CS99-1, University of New Mexico, Albuquerque (July 1999), http://www.cs.unm.edu/~bap/papers/sparse-ica-99a.ps.gz

  3. Yeredor, A.: Blind Source Separation with Pure Delay Mixtures. In: Proc. of ICA 2001, pp. 522–527 (2001)

    Google Scholar 

  4. Parra, L., Spence, C.: Blind Source Separation based on Multiple Decorrelations. In: IEEE Trans on Speech and Audio Processing, pp. 320–327 (May 2000)

    Google Scholar 

  5. Smaragdis, P.: Blind Separation of Convolved Mixtures in the Frequency Domain. In: Int. Worshop on Independence and ANN, Tenerife, Spain (February 1998)

    Google Scholar 

  6. Araki, S., Makino, S., Mukai, R., Nishikawa, T., Saruwatari, H.: Fundamental Limitation of Frequency Domain Blind Source Separation for Convolved Mixture of Speech. In: Proc. of ICA 2001, pp 132–137 (2001), Available at, http://www.kecl.ntt.co.jp/icl/signal/makino/

  7. Bofill, P., Zibulevsky, M.: Underdetermined Blind Source Separation using Sparse Representations. Signal Processing 81, 2353–2362 (2001), Preprint available at, http://www.ac.upc.es/homes/pau/

    Article  MATH  Google Scholar 

  8. Zibulevsky, M., Pearlmutter, B.A., Bofill, P., Kisiliev, P.: Blind Source Separation by Sparse Decomposition in a Signal Dictionary. In: Roberts, S.J., Everson, R.M. (eds.) Independent Component Analysis: Principles and Practice, ch. 7, pp. 181–208. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  9. Bofill, P.: Underdetermined Blind Separation of Delayed Sound Sources in the Frequency Domain. In: Fanni, A., Uncini, A. (eds.) Neurocomputing, Special issue: Evolving Solution with Neural Networks, October 2003, vol. 55(3-4), pp. 627–641 (2003), Preprint available at, http://www.ac.upc.es/homes/pau/

  10. Rickard, S., Balan, R., Rosca, J.: Real-Time Time-Frequency Based Blind Source Separation. In: Proc. of ICA 2001, pp. 651–656 (2001)

    Google Scholar 

  11. Araki, S., Sawada, H., Mukai, R., Makino, S.: A novel blind source separation method with observation vector clustering. In: Proc. IWAENC 2005, September 2005, pp. 117–120 (2005), Available at, http://www.kecl.ntt.co.jp/icl/signal/makino/

  12. Schroeder, M.R.: New Method of Measuring Reverberation Time. J. Acoust. Soc. Am. 37(3), 402–419 (1965)

    Article  Google Scholar 

  13. Bonavida, A.: Acustica, Course notes, Edited by Cpet, ETSETB-UPC (1979)

    Google Scholar 

  14. Lobo, M.S., Vandenberghe, L., Boyd, S., Lebret, H.: Applications of Second-order Cone Programming. Linear Algebra and its Applications 284, 193–228 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  15. Winter, S., Sawada, H., Makino, S.: On real and complex valued L1-norm minimization for overcomplete blind source separation. In: Proc. WASPAA 2005, October 2005, pp. 86–89 (2005), Available at, http://www.kecl.ntt.co.jp/icl/signal/makino/

  16. Lewicki, M.S., Sejnowski, T.J.: Learning overcomplete representations. Neural Computation 12(2), 337–365 (2000), Available at, citeseer.nj.nec.com/lewicki98learning.html

    Article  Google Scholar 

  17. McGovern, S.G., http://www.steve-m.us/code/fconv.m paper available at, http://www.steve-m.us/rir.html

  18. Sturm, J.F.: Using SeDuMi 1.0x, a Matlab Toolbox for Optimization over Symmetric Cones (1999), http://www.unimaas.nl/sturm

  19. Kinsler, L., Frey, A., Coppens, A., Sanders, J.: Fundamentals of Acoustics. John Wiley & Sons, Chichester (1989)

    Google Scholar 

  20. The Mathworks, Matlab/network toolbox

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departament d’Arquitectura de Computadors, UPC, Campus Nord, Mòdul D6, Jordi Girona 1-3, 08034, Barcelona, Spain

    Pau Bofill

  2. Departament de Teoria del Senyal i Comunicacions, UPC, Campus Nord, Mòdul D5, Jordi Girona 1-3, 08034, Barcelona, Spain

    Enric Monte

Authors
  1. Pau Bofill
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Enric Monte
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Siemens Corporate Research, 755 College Road East, 08540, Princeton, NJ, USA

    Justinian Rosca

  2. Department of CSEE, Oregon Health and Science University, Portland, Oregon, USA

    Deniz Erdogmus

  3. Dep. of Electrical and Computer Engineering, University of Florida, Gainesville, Florida, USA

    José C. Príncipe

  4. McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, Ontario, Canada

    Simon Haykin

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bofill, P., Monte, E. (2006). Underdetermined Convoluted Source Reconstruction Using LP and SOCP, and a Neural Approximator of the Optimizer. In: Rosca, J., Erdogmus, D., Príncipe, J.C., Haykin, S. (eds) Independent Component Analysis and Blind Signal Separation. ICA 2006. Lecture Notes in Computer Science, vol 3889. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11679363_71

Download citation

  • DOI: https://doi.org/10.1007/11679363_71

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32630-4

  • Online ISBN: 978-3-540-32631-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation