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
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Olshausen, B.A., Field, D.J.: Sparse coding with an overcomplete basis set: A strategy employed by V1? Vision Research 37, 3311–3325 (1997)
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
Yeredor, A.: Blind Source Separation with Pure Delay Mixtures. In: Proc. of ICA 2001, pp. 522–527 (2001)
Parra, L., Spence, C.: Blind Source Separation based on Multiple Decorrelations. In: IEEE Trans on Speech and Audio Processing, pp. 320–327 (May 2000)
Smaragdis, P.: Blind Separation of Convolved Mixtures in the Frequency Domain. In: Int. Worshop on Independence and ANN, Tenerife, Spain (February 1998)
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/
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/
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)
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/
Rickard, S., Balan, R., Rosca, J.: Real-Time Time-Frequency Based Blind Source Separation. In: Proc. of ICA 2001, pp. 651–656 (2001)
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/
Schroeder, M.R.: New Method of Measuring Reverberation Time. J. Acoust. Soc. Am. 37(3), 402–419 (1965)
Bonavida, A.: Acustica, Course notes, Edited by Cpet, ETSETB-UPC (1979)
Lobo, M.S., Vandenberghe, L., Boyd, S., Lebret, H.: Applications of Second-order Cone Programming. Linear Algebra and its Applications 284, 193–228 (1998)
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/
Lewicki, M.S., Sejnowski, T.J.: Learning overcomplete representations. Neural Computation 12(2), 337–365 (2000), Available at, citeseer.nj.nec.com/lewicki98learning.html
McGovern, S.G., http://www.steve-m.us/code/fconv.m paper available at, http://www.steve-m.us/rir.html
Sturm, J.F.: Using SeDuMi 1.0x, a Matlab Toolbox for Optimization over Symmetric Cones (1999), http://www.unimaas.nl/sturm
Kinsler, L., Frey, A., Coppens, A., Sanders, J.: Fundamentals of Acoustics. John Wiley & Sons, Chichester (1989)
The Mathworks, Matlab/network toolbox
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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)