TY - JOUR
T1 - Noise enhanced hypothesis-testing in the restricted Bayesian framework
AU - Bayram, Suat
AU - Gezici, Sinan
AU - Poor, H. Vincent
N1 - Funding Information:
Manuscript received November 06, 2009; accepted March 21, 2010. Date of publication April 12, 2010; date of current version July 14, 2010. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Z. Jane Wang. This research was supported in part by the U.S. Office of Naval Research under Grant N00014-09-1-0342. Part of this work was presented at the International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Dallas, TX, March 14–19, 2010.
PY - 2010/8
Y1 - 2010/8
N2 - 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.
AB - 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.
KW - Composite hypotheses
KW - M-ary hypothesis-testing
KW - noise enhanced detection
KW - restricted Bayes
KW - stochastic resonance
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U2 - 10.1109/TSP.2010.2048107
DO - 10.1109/TSP.2010.2048107
M3 - Article
AN - SCOPUS:77954575638
SN - 1053-587X
VL - 58
SP - 3972
EP - 3989
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 8
M1 - 5446401
ER -