Statistical and Information-Theoretic Methods for Self-Organization and Fusion of Multimodal,Networked Sensors

Abstract

The appeal of distributed sensing and computation is matched by the formidable challenges it presents in terms of estimation and communication. Applications range from military surveillance to collaborative office environments. Despite the attractiveness of exploiting networks of low-power and low-cost sensors, how to do so is a difficult problem. In this paper, we adopt a statistical viewpoint of such networks, and identify three key challenges. The first is to develop principled methods for low-level fusion of sensors measuring different modalities. We discuss an information-theoretic approach to sensor fusion, and present experimental results using audio and video data. The core component of this method is the learning of a nonparametric joint statistical model for the sensing modes. Secondly, we discuss how one might apply such a sensor fusion algorithm to acquire the relative geometry of a network of sensors using passively-sensed data. Specifically, we show how the fusion method previously developed can be used to find correspondences between pairs of long-baseline sensors. Finding such correspondences is, in general, the starting point for recovering the geometry. Finally, we discuss two iterative algorithms for performing inference on graphical models with cycles. Such models provide a flexible framework for constructing globally consistent statistical models from a set of local interactions. Importantly, the algorithms that we present allow information to be transmitted and processed in a distributed manner.

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References

Aji, S.M. , Horn, G. , and McEliece, R. On the convergence of iterative decoding on graphs with a single cycle. In Proceedings IEEE Intl. Symp. on Information Theory, page 276, Cambridge, MA, 1998.

Bertsekas, D. Dynamic programming and stochastic control, volume 1. Athena Scientific, Belmont, MA, 1995.

Besag, J. Spatial interaction and the statistical analysis of lattice systems. J. Roy. Stat. Soc. Series B, 36:192-236, 1974.

Besag, J. and Green, P.J. Spatial statistics and Bayesian computation. J. R. Stat. Soc. B, 55(1):25-37, 1993.

Chou, K. , Willsky, A. , and Nikoukhah, R. Multiscale systems, Kalman filters, and Riccati equations. IEEE Trans. AC, 39(3):479-492, March 1994.

Cooper, G. The computational complexity of probabilistic inference using Bayesian belief networks. Artificial Intelligence , 42:393-405, 1990.

Cover, T.M. and Thomas, J.A. Elements of Information Theory. John Wiley & Sons, Inc., New York, 1991.

Demmel, J. Applied numerical linear algebra. SIAM, Philadelphia, 1997.

Devroye, L. A Course in Density Estimation, volume 14 of Progress in Probability and Statistics . Birkhauser, Boston, 1987.

10.

Fisher, J. and Principe, J. Unsupervised learning for nonlinear synthetic discriminant functions. In Casasent, D. and Chao, T., editors, Proc. SPIE, Optical Pattern Recognition VII, volume 2752, pages 2-13, 1996.

11.

Fisher III, J.W. , Darrell, T. , Freeman, W.T. , and Viola, P. Learning joint statistical models for audio-visual fusion and segregation. In Advances in Neural Information Processing Systems 13, 2000.

12.

Fisher III, J.W. , Ihler, A.T. , and Viola, P.A. Learning informative statistics: A nonparametric approach. In Solla, S. A. , Leen, T. K. , and Müller, K.-R. , editors, Advances in Neural Information Processing Systems 12, 1999.

13.

Fisher III, J.W. and Principe, J.C. A methodology for information theoretic feature extraction. In A. Stuberud, editor, Proceedings of the IEEE International Joint Conference on Neural Networks, 1998.

14.

Freeman, W.T. , Pasztor, E.C. , and Carmichael , O.T.

Learning low-level vision

Intl. J. Computer Vision, 40(1):25-47, 2000.

15.

Frey, B. , Koetter, R. , and Petrovic, N. Very loopy belief propagation for unwrapping phase images. In NIPS 14. MIT Press, 2001.

16.

Jazwinski, A.H. Stochastic processes and filtering theory. Academic Press, New York, 1970.

17.

Jordan, M. , Ghahramani, Z. , Jaakkola, T.S. , and Saul, L. An introduction to variational methods for graphical models. In Learning in graphical models, pages 105-161. MIT Press, 1999.

18.

Kschischang, F. and Frey, B. Iterative decoding of compound codes by probability propagation in graphical models. IEEE Sel. Areas Comm., 16(2):219-230, February 1998.

19.

Kullback, S. Information Theory and Statistics. John Wiley and Sons , New York, 1959.

20.

Lauritzen, S.L. Graphical models. Oxford University Press, Oxford, 1996.

21.

McEliece, R. , McKay, D. , and Cheng, J. Turbo decoding as an instance of Pearl's belief propagation algorithm. IEEE Jour. Sel. Communication, 16(2):140-152, February 1998.

22.

Murphy, K. , Weiss, Y. , and Jordan, M. Loopy-belief propagation for approximate inference: An empirical study. In Uncertainty in Artificial Intelligence, volume 9, 1999.

23.

Parzen, E. On estimation of a probability density function and mode. Ann. of Math Stats., 33:1065-1076, 1962.

24.

Pearl, J. Probabilistic reasoning in intelligent systems. Morgan Kaufman, San Mateo, 1988.

25.

Richardson, T. The geometry of turbo-decoding dynamics. IEEE Trans. Info. Theory, 46(1):9-23, January 2000.

26.

Rusmevichientong, P. and Van Roy , B. An analysis of belief propagation on the turbo decoding graph with Gaussian densities. IEEE Trans. Info. Theory, 47(2): 745-765, Feb. 2001.

27.

Sudderth, E. Embedded trees: Estimation of Gaussian processes on graphs with cycles. Master's thesis, Massachusetts Institute of Technology, February 2002.

28.

Wainwright, M.J. Stochastic processes on graphs with cycles: geometric and variational approaches. PhD thesis, MIT, Laboratory for Information and Decision Systems, January 2002.

29.

Wainwright, M.J. , Jaakkola, T. , and Willsky, A.S. Tree-based reparameterization for approximate estimation on graphs with cycles. LIDS Tech. report P-2510: available at http://ssg.mit.edu/group/mjwain/mjwain.shtml, May 2001.

30.

Wainwright, M.J. , Jaakkola, T. , and Willsky, A.S. Tree-based reparameterization for approximate inference on loopy graphs. In NIPS 14. MIT Press, 2002.

31.

Wainwright, M.J. , Sudderth, E.B. , and Willsky, A.S. Tree-based modeling and estimation of Gaussian processes on graphs with cycles. In Advances in Neural Information Processing Systems 13, pages 661-667. MIT Press, 2001.

32.

Weiss, Y. Correctness of local probability propagation in graphical models with loops. Neural Computation, 12:1-41, 2000.

33.

Weiss, Y. and Freeman, W.T. Correctness of belief propagation in Gaussian graphical models of arbitrary topology. Neural Computation , 13:2173-2200, 2001.

34.

Yedidia, J. , Freeman, W.T. , and Weiss, Y. Generalized belief propagation. In NIPS 13, pages 689-695. MIT Press, 2001.