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Entropy 2016, 18(6), 213; doi:10.3390/e18060213

Optimal Noise Enhanced Signal Detection in a Unified Framework

College of Communication Engineering, Chongqing University, Chongqing 400044, China
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Academic Editors: Julio Stern and Adriano Polpo
Received: 22 February 2016 / Revised: 18 May 2016 / Accepted: 26 May 2016 / Published: 17 June 2016
(This article belongs to the Special Issue Statistical Significance and the Logic of Hypothesis Testing)
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Abstract

In this paper, a new framework for variable detectors is formulated in order to solve different noise enhanced signal detection optimal problems, where six different disjoint sets of detector and discrete vector pairs are defined according to the two inequality-constraints on detection and false-alarm probabilities. Then theorems and algorithms constructed based on the new framework are presented to search the optimal noise enhanced solutions to maximize the relative improvements of the detection and the false-alarm probabilities, respectively. Further, the optimal noise enhanced solution of the maximum overall improvement is obtained based on the new framework and the relationship among the three maximums is presented. In addition, the sufficient conditions for improvability or non-improvability under the two certain constraints are given. Finally, numerous examples are presented to illustrate the theoretical results and the proofs of the main theorems are given in the Appendix. View Full-Text
Keywords: signal detection; optimal noise; variable detector; different sets signal detection; optimal noise; variable detector; different sets
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Yang, T.; Liu, S.; Tang, M.; Zhang, K.; Zhang, X. Optimal Noise Enhanced Signal Detection in a Unified Framework. Entropy 2016, 18, 213.

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