Noise enhanced hypothesis-testing in the restricted Bayesian framework
Date
2010-04-12Source Title
IEEE Transactions on Signal Processing
Print ISSN
1053-587X
Publisher
IEEE
Volume
58
Issue
8
Pages
3972 - 3989
Language
English
Type
ArticleItem Usage Stats
130
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Abstract
Performance of some suboptimal detectors can be enhanced by adding independent noise to their observations. In this paper, the effects of additive noise are investigated according to the restricted Bayes criterion, which provides a generalization of the Bayes and minimax criteria. Based on a generic M-ary composite hypothesis-testing formulation, the optimal probability distribution of additive noise is investigated. Also, sufficient conditions under which the performance of a detector can or cannot be improved via additive noise are derived. In addition, simple hypothesis-testing problems are studied in more detail, and additional improvability conditions that are specific to simple hypotheses are obtained. Furthermore, the optimal probability distribution of the additive noise is shown to include at most M mass points in a simple M-ary hypothesis-testing problem under certain conditions. Then, global optimization, analytical and convex relaxation approaches are considered to obtain the optimal noise distribution. Finally, detection examples are presented to investigate the theoretical results.
Keywords
Composite hypothesesM-ary hypothesis-testing
Noise enhanced detection
Restricted Bayes
Stochastic resonance