Overcomplete Blind Source Separation for Time-Series Processes

10.29973/JCSA.200612.0001

Ray-Bing Chen；Shih-Wei Chiang

Autoregressive process ； Autoregressive and moving average process ； Null-space algorithm ； Overcomplete independent component analysis

中國統計學報

44卷4期（2006 / 12 / 01）

342 - 363

英文

Overcomplete blind source separation problems are considered here. The overcomplete situation is that the number of sources is greater than the number of receivers. In this work, sources are natural sounds, and time-series processes are used to characterized the statistical regularities of these natural sounds. The null-space algorithm is applied here to accomplish the source separation. We demonstrate several real examples based on two simple time-series processes. Finally we compare the separation results according to the different model assumptions.

1. Bell, A. J.,Sejnowski, T. J.(1995).An in formation maximization approach to blind separation and blind deconvolution.Neural Computation,7(6),1129-1159.
2. Bickel, P. J.,Levina, E.(2004).Some theory for Fisher`s linear discriminat function `naive Bayes`, and some alternative when there are many more variables than observations.Bernoulli,10(6),989-1010.
3. Box, G. E. P.,Jenkins, G. M.,Reinsel, G. C.(1994).Time Series Analysis: Forecasting and Control.Upper Saddle River, NJ:Prentice Hall.
4. Chen, R.-B.(2003).Los Angeles,Department of Statistics, University of California.
5. Chen, R.-B.,Wu, Y. N.(2004).A Null-space algorithm for Overcomplete Blind Source Separation, Technical Report, Institute of Statistics.National University of Kaohsiung.
6. Chen, R.-B.,Wu, Y. N.(2002).A Null-space Representation for Overcomplete Independent Component Analysis. 2002 Proceedings of American Statistical Association, Statistical Computing Section [CD-ROM].Alexandria, VA:American Statistical Association.
7. Comon, P.(1994).Independent component analysis-a new concept?.Signal Processing,36(3),287-314.
8. Godsill, S. J.(1997).Bayesian enhancement if speech and audio signals which can be modelled as ARMA processes.International Statistical Review,65(1),1-21.
9. Lee, T.-W.,Lewicki, M. S.,Girolami, M.,Sejnowski, T. J.(1999).Blind source separation of more source than mixtures using overcomplete representation.IEEE Signal Processing Letters,6(4),87-90.
10. Lewicki, M. S.,Sejnowski, T. J.(2000).Learning overcomplete representations.Neural Computation,12,337-365.
11. Pearlmutter, B.,Parra, L.(1996).A context-sensitive generalization of ICA.ICONIP.
12. Tanner, M.,Wong, W.(1987).The calculation of posterior distributions by data augmentation.Journal of the American Statistical Association,82,528-550.