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Time estimation for heat diffusion on graphs

Teke, Oguzhan and Vaidyanathan, P. P. (2017) Time estimation for heat diffusion on graphs. In: 2017 51st Asilomar Conference on Signals, Systems, and Computers. IEEE , Piscataway, NJ, pp. 1963-1967. ISBN 978-1-5386-1823-3. http://resolver.caltech.edu/CaltechAUTHORS:20180419-095409264

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Abstract

This paper studies the estimation of the starting time of a diffusion process from its noisy measurements when there is a single point source located on a known vertex of a graph with unknown starting time. The diffusion process is assumed to be governed by the heat equation. In particular, the Cramer-Rao lower bound (CRLB) for the problem is derived. It is shown that the problem has a larger CRLB for graphs with higher connectivity. Closed form expression of the bound is derived for some graphs. The ML estimator is numerically verified to be unbiased, and achieve the CRLB for some graphs.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/ACSSC.2017.8335709DOIArticle
https://ieeexplore.ieee.org/document/8335709PublisherArticle
ORCID:
AuthorORCID
Teke, Oguzhan0000-0002-1131-5206
Additional Information:© 2017 IEEE. This work was supported in parts by the ONR grants N00014-15-1-2118 and N00014-17-1-2732, the NSF grant CCF-1712633, and the Electrical Engineering Carver Mead Research Seed Fund of the California Institute of Technology.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-15-1-2118
Office of Naval Research (ONR)N00014-17-1-2732
NSFCCF-1712633
CaltechUNSPECIFIED
Subject Keywords:Diffusion process, heat equation, Cramér-Rao lower bound, graph signal processing
Record Number:CaltechAUTHORS:20180419-095409264
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180419-095409264
Official Citation:O. Teke and P. P. Vaidyanathan, "Time estimation for heat diffusion on graphs," 2017 51st Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, USA, 2017, pp. 1963-1967. doi: 10.1109/ACSSC.2017.8335709. URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=8335709&isnumber=8335116
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85971
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:19 Apr 2018 21:11
Last Modified:19 Apr 2018 21:11

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