Abstract
Sensor networks have emerged as a fundamentally new tool for monitoring spatially distributed phenomena. This paper investigates a strategy by which sensor nodes detect and estimate non-localized phenomena such as “boundaries” and “edges” (e.g., temperature gradients, variations in illumination or contamination levels). A general class of boundaries, with mild regularity assumptions, is considered, and theoretical bounds on the achievable performance of sensor network based boundary estimation are established. A hierarchical boundary estimation algorithm is proposed that achieves a near-optimal balance between mean-squared error and energy consumption.
Supported by the National Science Foundation, grant nos. MIP-9701692 and ANI-0099148, the Office of Naval Research, grant no. N00014-00-1-0390, and the Army Research Office, grant no. DAAD19-99-1-0290.
Supported by the Texas Instruments Visiting Professorship.
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References
L. Breiman, J. Friedman, R. Olshen, and C. J. Stone. Classification and Regression Trees. Wadsworth, Belmont, CA, 1983.
K. Chintalapudi and R. Govindan. Localized edge detection in sensor fields. University of Southern California, Computer Science Department, Technical Report, 02-773, 2002. available at http://www.cs.usc.edu/tech-reports/technical-reports.html.
D. Donoho. Wedgelets: Nearly minimax estimation of edges. Ann. Statist., 27:859–897, 1999.
D. Ganesan, D. Estrin, and J. Heideman. DIMENSIONS: Why do we need a new data handling architecture for sensor networks? In Proceedings of IEEE/ACM HotNets-I, Princeton, NJ, October 2002.
E. Kolaczyk and R. Nowak. Multiscale likelihood analysis and complexity penalized estimation. Annals of Statistics (tentatively accepted for publication). Also available at http://www.ece.rice.edu/~nowak/pubs.html, 2002.
A. P. Korostelev and A. B. Tsybakov. Minimax theory of image reconstruction. Springer-Verlag, New York, 1993.
B. Laurent and P. Massart. Adaptive estimation of a quadratic functional by model selection. The Annals of Statistics, (5), October 2000.
Q. Li and A. Barron. Mixture density estimation. In S.A. Solla, T.K. Leen, and K.-R. Müller, editors, Advances in Neural Information Processing Systems 12. MIT Press, 2000.
C. Scott and R. Nowak. Dyadic classification trees via structural risk minimization. In Proc. Neural Information Processing Systems (NIPS), Vancouver, CA, Dec. 2002.
R. Willett and R. Nowak. Platelets: A multiscale approach to recovering edges and surfaces in photon-limited imaging. IEEE Trans. Med. Imaging, to appear in the Special Issue on Wavelets in Medical Imaging, 2003.
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Nowak, R., Mitra, U. (2003). Boundary Estimation in Sensor Networks: Theory and Methods. In: Zhao, F., Guibas, L. (eds) Information Processing in Sensor Networks. IPSN 2003. Lecture Notes in Computer Science, vol 2634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36978-3_6
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DOI: https://doi.org/10.1007/3-540-36978-3_6
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