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      Noise enhanced hypothesis-testing in the restricted Bayesian framework

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      Author(s)
      Bayram, S.
      Gezici, Sinan
      Poor H. V.
      Date
      2010-04-12
      Source Title
      IEEE Transactions on Signal Processing
      Print ISSN
      1053-587X
      Publisher
      IEEE
      Volume
      58
      Issue
      8
      Pages
      3972 - 3989
      Language
      English
      Type
      Article
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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 hypotheses
      M-ary hypothesis-testing
      Noise enhanced detection
      Restricted Bayes
      Stochastic resonance
      Permalink
      http://hdl.handle.net/11693/22261
      Published Version (Please cite this version)
      http://dx.doi.org/10.1109/TSP.2010.2048107
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      • Department of Electrical and Electronics Engineering 3702
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