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Optimal Bi-Level Quantization of i.i.d. Sensor Observations for Binary Hypothesis Testing (2002)
| Venue: | IEEE Trans. Inform. Theory |
| Citations: | 15 - 2 self |
BibTeX
@ARTICLE{Zhang02optimalbi-level,
author = {Qian Zhang and Pramod K. Varshney and Richard D. Wesel and Senior Member},
title = {Optimal Bi-Level Quantization of i.i.d. Sensor Observations for Binary Hypothesis Testing},
journal = {IEEE Trans. Inform. Theory},
year = {2002},
volume = {48},
pages = {21052111}
}
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Abstract
We consider the problem of binary hypothesis testing using binary decisions from independent and identically distributed (i.i.d). sensors. Identical likelihood-ratio quantizers with threshold are used at the sensors to obtain sensor decisions. Under this condition, the optimal fusion rule is known to be a-out-of- rule with threshold . For the Bayesian detection problem, we show that given , the probability of error is a quasiconvex function of and has a single minimum that is achieved by the unique optimal . Except for the trivial situation where one hypothesis is always decided, we obtain a sufficient and necessary condition on , and show that can be efficiently obtained via the SECANT algorithm. The overall optimal solution is obtained by optimizing every pair of ( ). For the Neyman--Pearson detection problem, we show that the use of the Lagrange multiplier method is justified for a given fixed since the objective function is a quasi-convex function of . We further show that the receiver operating characteristic (ROC) for a fixed is concave downward.
Keyphrases
binary hypothesis testing optimal bi-level quantization sensor observation a-out-of rule lagrange multiplier method binary decision overall optimal solution binary hypothesis trivial situation quasiconvex function single minimum sensor decision identical likelihood-ratio quantizers neyman pearson detection problem secant algorithm necessary condition bayesian detection problem optimal fusion rule quasi-convex function objective function unique optimal
