Abstract
Blind Source Separation consists of estimating n sources from the measurements provided by m sensors. In this paper we deal with the underdetermined case, m < n, where the solution can be implemented in two stages: first estimate the mixing matrix from the measurements and then estimate the best solution to the underdetermined linear problem. Instead of being restricted to the conventional two-measurements scenario, in this paper we propose a technique that is able to deal with this underdetermined linear problem at an arbitrary number of dimensions. The key points of our procedure are: to parametrize the mixing matrix in spherical coordinates, to estimate the projections of the maxima of the multidimensional PDF that describes the mixing angles through the marginals, and to reconstruct the maxima in the multidimensional space from the projections. The results presented compare the proposed approach with estimation using multidimensional ESPRIT.
This work has been partially supported by Spanish Ministry of Science and Technology under project TIC2001-0751-C04-03.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. John Wiley & Sons, New York (2001)
Haykin, S. (ed.): Unsupervised Adaptive Filtering. Blind Source Separation, vol. I. John Wiley & Sons, New York (2000)
Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. Johns Hopkins University Press, Baltimore (1996)
Vielva, L., Erdoğmuş, D., Príncipe, J.C.: Underdetermined blind source separation in a time-varying environment. In: Proceedings ICASSP 2002 (IEEE International Conference on Acoustics, Speech and Signal Processing), Orlando, FL, May 2002, pp. 3049–3052 (2002)
Zibulevsky, M., Pearlmutter, B., Bofill, P., Kisilev, P.: Blind source separation by sparse decomposition in a signal dictionary. In: Independent Components Analysis: Principles and Practice, Cambridge University Press, Cambridge (2000)
Bofill, P., Zibulevsky, M.: Underdetermined blind source separation using sparse representations. Signal Processing 81(11), 2353–2362 (2001)
Erdoğmuş, D., Vielva, L., Príncipe, J.C.: Nonparametric estimation and tracking of the mixing matrix for underdetermined blind source separation. In: Proceedings of ICA 2001, Independent Component Analysis, San Diego, CA, December 2001, pp. 189–193 (2001)
Vielva, L., Erdoğmuş, D., Príncipe, J.C.: Underdetermined blind source separation using a probabilistic source sparsity model. In: Proceedings of ICA 2001, Independent Component Analysis, San Diego, CA, December 2001, pp. 675–679 (2001)
Puntonet, C.G., Prieto, A., Jutten, C., Rodriguez-Alvarez, M., Ortega, J.: Separation of sources: A geometry-based procedure for reconstruction of n-valued signals. IEEE Trans. on Acoustics, Speech, and Signal Processing 46(3), 267–284 (1995)
Jung, A., Theis, F., Puntonet, C., Lang, E.: Fastgeo - a histogram based approach to linear geometric ICA. In: Independent Component Analysis, San Diego. CA, pp. 349–354 (2001)
Theodoridis, S., Koutroumbas, K.: Pattern Recognition. Academic Press, San Diego (1999)
Vielva, L., Santamaría, I., Pantaleón, C., Ibáñez, J., Erdoğmuş, D., Príncipe, J.C.: Estimation of the mixing matrix for underdetermined blind source separation using spectral estimation techniques. In: Proceedings Eusipco-2002 (XI European Signal Processing Conference), Toulouse, France, September 3-6, vol. I, pp. 557–560 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Vielva, L., Santamaría, I., Ibáñez, J., Erdogmus, D., Príncipe, J.C. (2004). On the Estimation of the Mixing Matrix for Underdetermined Blind Source Separation in an Arbitrary Number of Dimensions. In: Puntonet, C.G., Prieto, A. (eds) Independent Component Analysis and Blind Signal Separation. ICA 2004. Lecture Notes in Computer Science, vol 3195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30110-3_24
Download citation
DOI: https://doi.org/10.1007/978-3-540-30110-3_24
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23056-4
Online ISBN: 978-3-540-30110-3
eBook Packages: Springer Book Archive