{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:00:45Z","timestamp":1760241645764,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2018,6,17]],"date-time":"2018-06-17T00:00:00Z","timestamp":1529193600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61701055"],"award-info":[{"award-number":["61701055"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012334","name":"Graduate scientific research and innovation foundation of Chongqing","doi-asserted-by":"publisher","award":["CYB17041"],"award-info":[{"award-number":["CYB17041"]}],"id":[{"id":"10.13039\/501100012334","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Basic and Advanced Research Project in Chongqing","award":["cstc2016jcyjA0134 and cstc2016jcyjA0043"],"award-info":[{"award-number":["cstc2016jcyjA0134 and cstc2016jcyjA0043"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, a noise enhanced binary hypothesis-testing problem was studied for a variable detector under certain constraints in which the detection probability can be increased and the false-alarm probability can be decreased simultaneously. According to the constraints, three alternative cases are proposed, the first two cases concerned minimization of the false-alarm probability and maximization of the detection probability without deterioration of one by the other, respectively, and the third case was achieved by a randomization of two optimal noise enhanced solutions obtained in the first two limit cases. Furthermore, the noise enhanced solutions that satisfy the three cases were determined whether randomization between different detectors was allowed or not. In addition, the practicality of the third case was proven from the perspective of Bayes risk. Finally, numerous examples and conclusions are presented.<\/jats:p>","DOI":"10.3390\/e20060470","type":"journal-article","created":{"date-parts":[[2018,6,18]],"date-time":"2018-06-18T10:57:11Z","timestamp":1529319431000},"page":"470","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Noise Enhanced Signal Detection of Variable Detectors under Certain Constraints"],"prefix":"10.3390","volume":"20","author":[{"given":"Ting","family":"Yang","sequence":"first","affiliation":[{"name":"College of Communication Engineering, Chongqing University, Chongqing 400044, China"}]},{"given":"Shujun","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Communication Engineering, Chongqing University, Chongqing 400044, China"}]},{"given":"Wenguo","family":"Liu","sequence":"additional","affiliation":[{"name":"Chongqing Institution of Tuberculosis Treatment and Prevention, Chongqing 400050, China"}]},{"given":"Jishun","family":"Guo","sequence":"additional","affiliation":[{"name":"GAC Automotive Engineering Institute, Guangzhou 510640, China"}]},{"given":"Pin","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Communication Engineering, Chongqing University, Chongqing 400044, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,6,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1088\/0305-4470\/14\/11\/006","article-title":"The mechanism of stochastic resonance","volume":"14","author":"Benzi","year":"1981","journal-title":"J. Phys. A Math. Gen."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.dsp.2015.03.016","article-title":"Noise enhanced binary hypothesis-testing in a new framework","volume":"41","author":"Liu","year":"2015","journal-title":"Digit. Signal Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1109\/TNANO.2006.883476","article-title":"Noise-enhanced detection of subthreshold signals with carbon nanotubes","volume":"5","author":"Lee","year":"2006","journal-title":"IEEE Trans. Nanotechnol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1103\/PhysRevE.61.233","article-title":"Stochastic resonance as dithering","volume":"61","author":"Wannamaker","year":"2000","journal-title":"Phys. Rev. E"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"115001","DOI":"10.1088\/0957-0233\/23\/11\/115001","article-title":"Multiscale noise tuning stochastic resonance enhances weak signal detection in a circuitry system","volume":"23","author":"Dai","year":"2012","journal-title":"Meas. Sci. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"218103","DOI":"10.1103\/PhysRevLett.90.218103","article-title":"Behavioral stochastic resonance within the human brain","volume":"90","author":"Kitajo","year":"2003","journal-title":"Phys. Rev. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/j.clinph.2003.09.014","article-title":"Stochastic resonance and sensory information processing: A tutorial and review of applications","volume":"115","author":"Moss","year":"2004","journal-title":"Clin. Neurophys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1993","DOI":"10.1109\/TNN.2008.2005610","article-title":"Stochastic resonance in continuous and spiking neuron models with Levy noise","volume":"19","author":"Patel","year":"2008","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"061105","DOI":"10.1103\/PhysRevE.75.061105","article-title":"Optimal stimulus and noise distributions for information transmission via suprathreshold stochastic resonance","volume":"75","author":"McDonnell","year":"2007","journal-title":"Phys. Rev. E"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Gagrani, M., Sharma, P., Iyengar, S., Nadendla, V.S., Vempaty, A., Chen, H., and Varshney, P.K. (2011, January 28\u201330). On Noise-Enhanced Distributed Inference in the Presence of Byzantines. Proceedings of the Annual Allerton Conference on Communication, Control, and Computing (Allerton), Monticello, IL, USA.","DOI":"10.1109\/Allerton.2011.6120307"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"L181","DOI":"10.1142\/S0219477501000408","article-title":"High signal-to-noise ratio gain by stochastic resonance in a double well","volume":"1","author":"Gingl","year":"2001","journal-title":"Fluctuat. Noise Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"L145","DOI":"10.1142\/S0219477502000750","article-title":"Signal-to-noise ratio gain in non-dynamical and dynamical bistable stochastic resonators","volume":"2","author":"Makra","year":"2002","journal-title":"Fluctuat. Noise Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.physleta.2003.08.042","article-title":"Signal-to-noise ratio gain in stochastic resonators driven by coloured noises","volume":"317","author":"Makra","year":"2003","journal-title":"Phys. Lett. A"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2310","DOI":"10.1103\/PhysRevLett.84.2310","article-title":"Suprathreshold stochastic resonance in multilevel threshold systems","volume":"84","author":"Stocks","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1142\/S0218127498000371","article-title":"Stochastic resonance in the information capacity of a nonlinear dynamic system","volume":"8","author":"Godivier","year":"1998","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1016\/S0893-6080(03)00128-X","article-title":"Stochastic resonance in noisy threshold neurons","volume":"16","author":"Kosko","year":"2003","journal-title":"Neural Netw."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"031911","DOI":"10.1103\/PhysRevE.70.031911","article-title":"Robust stochastic resonance for simple threshold neurons","volume":"70","author":"Kosko","year":"2004","journal-title":"Phys. Rev. E"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1526","DOI":"10.1109\/TNN.2004.826218","article-title":"Adaptive stochastic resonance in noisy neurons based on mutual information","volume":"15","author":"Mitaim","year":"2004","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3972","DOI":"10.1109\/TSP.2010.2048107","article-title":"Noise enhanced hypothesis-testing in the restricted bayesian framework","volume":"58","author":"Bayram","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Bayram, S., and Gezici, S. (2009, January 28\u201330). Noise-enhanced M-ary hypothesis-testing in the mini-max framework. Proceedings of the 3rd International Conference on Signal Processing and Communication Systems, Omaha, NE, USA.","DOI":"10.1109\/ICSPCS.2009.5306400"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1292","DOI":"10.1109\/TSP.2010.2097257","article-title":"Noise enhanced M-ary composite hypothesis-testing in the presence of partial prior information","volume":"59","author":"Bayram","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1109\/LSP.2006.879455","article-title":"Reducing probability of decision error using stochastic resonance","volume":"13","author":"Kay","year":"2006","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1109\/97.809511","article-title":"Can detectability be improved by adding noise","volume":"7","author":"Kay","year":"2000","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3172","DOI":"10.1109\/TSP.2007.893757","article-title":"Theory of the stochastic resonance effect in signal detection: Part I\u2014Fixed detectors","volume":"55","author":"Chen","year":"2007","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5031","DOI":"10.1109\/TSP.2008.928509","article-title":"Theory of the stochastic resonance effect in signal detection: Part II\u2014Variable detectors","volume":"56","author":"Chen","year":"2007","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1109\/TIT.2008.2009813","article-title":"Noise enhanced nonparametric detection","volume":"55","author":"Chen","year":"2009","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1655","DOI":"10.1109\/TSP.2009.2012893","article-title":"Optimal noise benefits in Neyman\u2013Pearson and inequality constrained signal detection","volume":"57","author":"Patel","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1016\/j.dsp.2012.02.003","article-title":"Stochastic resonance in binary composite hypothesis-testing problems in the Neyman\u2013Pearson framework","volume":"22","author":"Bayram","year":"2012","journal-title":"Digit. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1109\/LSP.2013.2271847","article-title":"One-bit decentralized detection with a Rao test for multisensor fusion","volume":"20","author":"Ciuonzo","year":"2013","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"678","DOI":"10.1109\/LSP.2017.2686377","article-title":"Generalized rao test for decentralized detection of an uncooperative target","volume":"24","author":"Ciuonzo","year":"2017","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1457","DOI":"10.1109\/TSP.2009.2036065","article-title":"Channel-aware decision fusion with unknown local sensor detection probability","volume":"58","author":"Wu","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1109\/LSP.2013.2295054","article-title":"Decision fusion with unknown sensor detection probability","volume":"21","author":"Ciuonzo","year":"2014","journal-title":"IEEE Signal Process. Lett."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/6\/470\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:09:06Z","timestamp":1760195346000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/6\/470"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,17]]},"references-count":32,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2018,6]]}},"alternative-id":["e20060470"],"URL":"https:\/\/doi.org\/10.3390\/e20060470","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2018,6,17]]}}}