Detection of Gauss-Markov Random Fields With Nearest-Neighbor Dependency
Abstract
The problem of hypothesis testing against independence for a Gauss-Markov random field (GMRF) is analyzed. Assuming an acyclic dependency graph, an expression for the log-likelihood ratio of detection is derived. Assuming random placement of nodes over a large region according to the Poisson or uniform distribution and nearest-neighbor dependency graph, the error exponent of the Neyman-Pearson detector is derived using large-deviations theory. The error exponent is expressed as a dependency-graph functional and the limit is evaluated through a special law of large numbers for stabilizing graph functionals. The exponent is analyzed for different values of the variance ratio and correlation. It is found that a more correlated GMRF has a higher exponent at low values of the variance ratio whereas the situation is reversed at high values of the variance ratio.
Additional Information
© 2009 IEEE. Manuscript received January 02, 2007; revised January 31, 2008. Current version published February 04, 2009. This work was supported in part through the collaborative participation in the Communications and Networks Consortium sponsored by the U.S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0011 and by the Army Research Office under Grant ARO-W911NF-06-1-0346. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon. The material in this paper was presented in part at IEEE International Conference on Acoustics, Speech and Signal Processing, Hawaii, April 2007.Attached Files
Published - 04777634.pdf
Submitted - 0706.1588.pdf
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Additional details
- Eprint ID
- 81659
- Resolver ID
- CaltechAUTHORS:20170920-162015185
- DAAD19-01-2-0011
- Army Research Laboratory (ARL)
- W911NF-06-1-0346
- Army Research Office (ARO)
- Created
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2017-09-20Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field