Stochastic resonance in binary composite hypothesis-testing problems in the Neyman-Pearson framework

Performance of some suboptimal detectors can be enhanced by adding independent noise to their inputs via the stochastic resonance (SR) effect. In this paper, the effects of SR are studied for binary composite hypothesis-testing problems. A Neyman-Pearson framework is considered, and the maximization of detection performance under a constraint on the maximum probability of false-alarm is studied. The detection performance is quantified in terms of the sum, the minimum, and the maximum of the detection probabilities corresponding to possible parameter values under the alternative hypothesis. Sufficient conditions under which detection performance can or cannot be improved are derived for each case. Also, statistical characterization of optimal additive noise is provided, and the resulting false-alarm probabilities and bounds on detection performance are investigated. In addition, optimization theoretic approaches to obtaining the probability distribution of optimal additive noise are discussed. Finally, a detection example is presented to investigate the theoretical results. © 2012 Elsevier Inc. All rights reserved

Noise Enhanced M-ary Composite Hypothesis-Testing in the Presence of Partial Prior Information

Cataloged from PDF version of article.In this correspondence, noise enhanced detection is studied for M-ary composite hypothesis-testing problems in the presence of partial prior information. Optimal additive noise is obtained according to two criteria, which assume a uniform distribution (Criterion 1) or the least-favorable distribution (Criterion 2) for the unknown priors. The statistical characterization of the optimal noise is obtained for each criterion. Specifically, it is shown that the optimal noise can be represented by a constant signal level or by a randomization of a finite number of signal levels according to Criterion 1 and Criterion 2, respectively. In addition, the cases of unknown parameter distributions under some composite hypotheses are considered, and upper bounds on the risks are obtained. Finally, a detection example is provided in order to investigate the theoretical results. © 2010 IEEE

Noise Enhanced Hypothesis-Testing in the Restricted Bayesian Framework

Cataloged from PDF version of article.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 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

Noise enhanced hypothesis-testing according to restricted Neyman-Pearson criterion

Cataloged from PDF version of article.Noise enhanced hypothesis-testing is studied according to the restricted Neyman-Pearson (NP) criterion. First, a problem formulation is presented for obtaining the optimal probability distribution of additive noise in the restricted NP framework. Then, sufficient conditions for improvability and nonimprovability are derived in order to specify if additive noise can or cannot improve detection performance over scenarios in which no additive noise is employed. Also, for the special case of a finite number of possible parameter values under each hypothesis, it is shown that the optimal additive noise can be represented by a discrete random variable with a certain number of point masses. In addition, particular improvability conditions are derived for that special case. Finally, theoretical results are provided for a numerical example and improvements via additive noise are illustrated. © 2013 Elsevier Inc

Effects of additional independent noise in binary composite hypothesis-testing problems

Performance of some suboptimal detectors can be improved by adding independent noise to their observations. In this paper, the effects of adding independent noise to observations of a detector are investigated for binary composite hypothesistesting problems in a generalized Neyman-Pearson framework. Sufficient conditions are derived to determine when performance of a detector can or cannot be improved via additional independent noise. Also, upper and lower limits are derived on the performance of a detector in the presence of additional noise, and statistical characterization of optimal additional noise is provided. In addition, two optimization techniques are proposed to calculate the optimal additional noise. Finally, simulation results are presented to investigate the theoretical results. © 2009 IEEE

Noise enhanced detection in restricted Neyman-Pearson framework

Noise enhanced detection is studied for binary composite hypothesis-testing problems in the presence of prior information uncertainty. The restricted Neyman-Pearson (NP) framework is considered, and a formulation is obtained for the optimal additive noise that maximizes the average detection probability under constraints on worst-case detection and false-alarm probabilities. In addition, sufficient conditions are provided to specify when the use of additive noise can or cannot improve performance of a given detector according to the restricted NP criterion. A numerical example is presented to illustrate the improvements obtained via additive noise. © 2012 IEEE

Noise enhanced detection in restricted Neyman-Pearson framework

Ankara : The Department of Electrical and Electronics Engineering and the Graduate School of Engineering and Science of Bilkent University, 2013.Thesis (Master's) -- Bilkent University, 2013.Includes bibliographical references leaves 37-40.Hypothesis tests frequently arise in many different engineering problems. Among the most frequently used tests are Bayesian, minimax, and Neyman-Pearson. Even though these tests are capable of addressing many real-life problems, they can be insufficient in certain scenarios. For this reason, developing new hypothesis tests is an important objective. One such developed test is the restricted NeymanPearson test, where one tries to maximize the average detection probability while keeping the worst-case detection and false-alarm probabilities bounded. Finding the best hypothesis testing approach for a problem-at-hand is an important point. Another important one is to employ a detector with an acceptable performance. In particular, if the employed detector is suboptimal, it is crucial that it meets the performance requirements. Previous research has proven that performance of some suboptimal detectors can be improved by adding noise to their inputs, which is known as noise enhancement. In this thesis we investigate noise enhancement according to the restricted Neyman-Pearson framework. To that aim, we formulate an optimization problem for optimal additive noise. Then, generic improvability and nonimprovability conditions are derived, which specify if additive noise can result in performance improvements. We then analyze the special case in which the parameter space is discrete and finite, and show that the optimal noise probability density function is discrete with a certain number of point masses. The improvability results are also extended and more precise conditions are derived. Finally, a numerical example is provided which illustrates the theoretical results and shows the benefits of applying noise enhancement to a suboptimal detector.Gültekin, ŞanM.S

Alternative approaches and noise benefits in hypothesis-testing problems in the presence of partial information

Ankara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent University, 2011.Thesis (Ph. D.) -- Bilkent University, 2011.Includes bibliographical references leaves 153-164.Performance of some suboptimal detectors can be enhanced by adding independent noise to their observations. In the first part of the dissertation, the effects of additive noise are studied 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. In the second part of the dissertation, the effects of additive noise are studied for M-ary composite hypothesis-testing problems in the presence of partial prior information. Optimal additive noise is obtained according to two criteria, which assume a uniform distribution (Criterion 1) or the least-favorable distribution (Criterion 2) for the unknown priors. The statistical characterization of the optimal noise is obtained for each criterion. Specifically, it is shown that the optimal noise can be represented by a constant signal level or by a randomization of a finite number of signal levels according to Criterion 1 and Criterion 2, respectively. In addition, the cases of unknown parameter distributions under some composite hypotheses are considered, and upper bounds on the risks are obtained. Finally, a detection example is provided to illustrate the theoretical results. In the third part of the dissertation, the effects of additive noise are studied for binary composite hypothesis-testing problems. A Neyman-Pearson (NP) framework is considered, and the maximization of detection performance under a constraint on the maximum probability of false-alarm is studied. The detection performance is quantified in terms of the sum, the minimum and the maximum of the detection probabilities corresponding to possible parameter values under the alternative hypothesis. Sufficient conditions under which detection performance can or cannot be improved are derived for each case. Also, statistical characterization of optimal additive noise is provided, and the resulting false-alarm probabilities and bounds on detection performance are investigated. In addition, optimization theoretic approaches for obtaining the probability distribution of optimal additive noise are discussed. Finally, a detection example is presented to investigate the theoretical results. Finally, the restricted NP approach is studied for composite hypothesistesting problems in the presence of uncertainty in the prior probability distribution under the alternative hypothesis. A restricted NP decision rule aims to maximize the average detection probability under the constraints on the worstcase detection and false-alarm probabilities, and adjusts the constraint on the worst-case detection probability according to the amount of uncertainty in the prior probability distribution. Optimal decision rules according to the restricted NP criterion are investigated, and an algorithm is provided to calculate the optimal restricted NP decision rule. In addition, it is observed that the average detection probability is a strictly decreasing and concave function of the constraint on the minimum detection probability. Finally, a detection example is presented, and extensions to more generic scenarios are discussed.Bayram, SuatPh.D

Noise enhanced detection

Ankara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent University, 2009.Thesis (Master's) -- Bilkent University, 2009.Includes bibliographical references leaves 64-67.Performance of some suboptimal detectors can be improved by adding independent noise to their measurements. Improving the performance of a detector by adding a stochastic signal to the measurement can be considered in the framework of stochastic resonance (SR), which can be regarded as the observation of “noise benefits” related to signal transmission in nonlinear systems. Such noise benefits can be in various forms, such as a decrease in probability of error, or an increase in probability of detection under a false-alarm rate constraint. The main focus of this thesis is to investigate noise benefits in the Bayesian, minimax and Neyman-Pearson frameworks, and characterize optimal additional noise components, and quantify their effects. In the first part of the thesis, a Bayesian framework is considered, and the previous results on optimal additional noise components for simple binary hypothesis-testing problems are extended to M-ary composite hypothesis-testing problems. In addition, a practical detection problem is considered in the Bayesian framework. Namely, binary hypothesis-testing via a sign detector is studied for antipodal signals under symmetric Gaussian mixture noise, and the effects of shifting the measurements (observations) used by the sign detector are investigated. First, a sufficient condition is obtained to specify when the sign detectorbased on the modified measurements (called the “modified” sign detector) can have smaller probability of error than the original sign detector. Also, two suf- ficient conditions under which the original sign detector cannot be improved by measurement modification are derived in terms of desired signal and Gaussian mixture noise parameters. Then, for equal variances of the Gaussian components in the mixture noise, it is shown that the probability of error for the modified detector is a monotone increasing function of the variance parameter, which is not always true for the original detector. In addition, the maximum improvement, specified as the ratio between the probabilities of error for the original and the modified detectors, is specified as 2 for infinitesimally small variances of the Gaussian components in the mixture noise. Finally, numerical examples are presented to support the theoretical results, and some extensions to the case of asymmetric Gaussian mixture noise are explained. In the second part of the thesis, the effects of adding independent noise to measurements are studied for M-ary hypothesis-testing problems according to the minimax criterion. It is shown that the optimal additional noise can be represented by a randomization of at most M signal values. In addition, a convex relaxation approach is proposed to obtain an accurate approximation to the noise probability distribution in polynomial time. Furthermore, sufficient conditions are presented to determine when additional noise can or cannot improve the performance of a given detector. Finally, a numerical example is presented. Finally, the effects of additional independent noise are investigated in the Neyman-Pearson framework, and various sufficient conditions on the improvability and the non-improvability of a suboptimal detector are derived. First, a sufficient condition under which the performance of a suboptimal detector cannot be enhanced by additional independent noise is obtained according to the Neyman-Pearson criterion. Then, sufficient conditions are obtained to specifywhen the detector performance can be improved. In addition to a generic condition, various explicit sufficient conditions are proposed for easy evaluation of improvability. Finally, a numerical example is presented and the practicality of the proposed conditions is discussed.Bayram, SuatM.S

Noise benefits in joint detection and estimation problems

Adding noise to inputs of some suboptimal detectors or estimators can improve their performance under certain conditions. In the literature, noise benefits have been studied for detection and estimation systems separately. In this study, noise benefits are investigated for joint detection and estimation systems. The analysis is performed under the Neyman-Pearson (NP) and Bayesian detection frameworks and according to the Bayesian estimation criterion. The maximization of the system performance is formulated as an optimization problem. The optimal additive noise is shown to have a specific form, which is derived under both NP and Bayesian detection frameworks. In addition, the proposed optimization problem is approximated as a linear programming (LP) problem, and conditions under which the performance of the system can or cannot be improved via additive noise are obtained. With an illustrative numerical example, performance comparison between the noise enhanced system and the original system is presented to support the theoretical analysis. © 2015 Elsevier B.V. All rights reserved