脉冲发放神经元及其耦合系统的随机模型研究与应用
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摘要
随着物理、数学、生物、计算机等科学的发展,人类对大脑的认识和研究越来越深入,特别是对神经模型的研究。科学家希望通过神经模型的研究揭开大脑的信息存储和处理机制,建立具有认知功能的脑模型,直至实现人工智能。科学研究一般遵循从简单到复杂的规律,因此本文以脉冲发放神经元模型为基本研究对象,对这类神经元的非线性动力学特征和信号传输等问题进行了研究,特别探索了噪声在模型的信号传输和处理中扮演的角色。结果表明噪声在神经元模型及其耦合系统中通过随机共振现象起到了有益的作用,还可以提高图像处理的效果;根据计算结果分析了信号在神经模型中的传输特性,希望有助于揭开神经系统的信号传输机制;并且这些模型及其结果还可以从模型的角度解释神经系统的生物和生理实验现象,对实验和某些疾患的医治具有指导意义。
本文的主要研究内容和成果为:
1、综合分析了近年来对脉冲发放神经元及其网络模型的研究,特别是其中的随机共振问题,对HH、FN神经元模型的放电特征和非线性动力学特征进行了研究。
2、在HH神经元随机模型中研究了噪声和高频信号的作用机制,强噪声导致的HH神经元长时放电,从模型角度解释了噪声引起耳鸣时听神经的自放电;噪声与高频的协作结果——高频信号对神经元放电有抑制,与生理实验结果一致,也表明神经系统中信号传输存在类似于听觉系统的双音遏制现象,即强度大的频率成分遏制强度低的频率成分;另外高频信号还导致神经元静息电位变为高频振荡,这些结果有助于开展神经系统的高频电磁场损伤治疗和防护研究。
3、对阈上单频和多频信号在HH神经元随机模型中的研究表明存在阈上随机共振现象,即适当强度的噪声同样有助于阈上信号的传输;神经元具有频率敏感性,类似于带通特性,且噪声强度可以改变神经元的敏感频率,即带通中心频率偏移,这些特点对于信号处理的研究具有重要意义。另外模型和结果与听觉系统的频率选择性特征相似,据此可以探讨听觉神经元频率选择的机制。
4、对阈下信号在FN神经元随机模型中的传输特性进行了研究和分析,结果不仅显示了随机共振的存在,还揭示FN神经元模型对正弦信号的传输与其频率密切相关,对频率处于0.2~0.8的正弦信号响应最强烈。此模型及结果可用于听神经纤维自发放电现象的解释。
5、HH单向耦合随机系统中的弱信号传输特性研究表明噪声通过随机共振使得系统实现了弱信号的检测和传输;适当的耦合强度和噪声强度可以实现神经滞后同步和最优的信息传递,并对此处的滞后同步进行了重定义和分析;在100个FN神经元构成的单向耦合随机系统中也发现了滞后同步的存在;另外模型仿真中出现的强耦合自放电及其被噪声抑制,有助于解释生物神经系统中神经元的自放电与其自我调制等现象。
6、首次对HH单向耦合随机系统的频率敏感性进行了分析,特别是接收元的行为,发现其敏感频率随噪声强度和耦合强度变化改变。多频叠加信号的结果与单频信号传输时一致,且噪声有碍于频率敏感性的表达。这些结果说明单向耦合系统也是一种带通器件,可通过改变自身的参数实现对某些频率的信号的最优传输。鉴于单向耦合网络源于中枢模式发生器,结果可用于解释它的节律发生机制。
7、首次通过PCNN随机模型研究了二维图像信号的处理中噪声扮演的角色,在高斯噪声图像滤波和低对比度图像的增强过程中均出现了随机共振现象,图像处理的效果得到了提高。因此拓展了随机共振的模型研究范围,有助于新的图像处理方法的研究。
With the development of physics, math, biology and computer, the investigation on brain has gained great achievements, especially the research on neural model. Scientists work on all kinds of neural models, trying to disclose the signal storing and processing of the brain, build brain model of cognition and realize the annual intelligence at last. Usually the scientific research begins from simple to complex, so the spiking neuron models and their coupled neural nets were selected as the main subject of this dissertation. Their nonlinear dynamic characteristics and signal transmission were studied. The role of noise was also discussed in the signal processing of the neuron models and net. The results show that noise is helpful to the signal processing through stochastic resonance. The characteristics of signal transmission were analyzed to reveal the neuron’s signal processing mechanism. These results are a kind of explanation of neural biological and physiological experiments in the models, are of significance to the experiments and treatments of some neural diseases.
The main contents and results of this thesis are as follows:
1. The studies on spiking neuron and net in recent years were reviewed, especially stochastic resonance in neural models. The firing characteristics and nonlinear dynamics of Hodgkin-Huxley (HH) and FitzHugh-Nagumo (FN) spiking neuron models were investigated.
2. The effects of high frequency (HF) signal on HH neuron stochastic model were studied. The HF signal inhibited the spiking of neuron, which was consistent with the physiological results. It was also similar with the two-tone suppression of auditory neuron. In addition, the HF signal could induce the resting potential change into high frequency oscillation. These results may be used to explain the corresponding physiological phenomenon.
3. The transmission of suprathreshold signal and multi- frequencies signals in the stochastic HH neuron model was investigated. Their transmission was influenced by noise through suprathreshold stochastic resonance. The model was of frequency sensitivity, similar to bandpass. It was alike the characteristics of auditory system, so it could be used to discuss the frequency selectivity of auditory neuron. The noise could change the sensitive frequency, i.e., the shift of center frequency of bandpass. It is of significance to signal processing method.
4. The transmission of subthreshold signal in FN stochastic model was investigated. The results showed that there was stochastic resonance and the transmission of sinusoidal signal was closely correlated with its frequency. The neuron model responded strongly with frequencies in the range of 0.2~0.8. Accordingly, the self firing activity of auditory neuron was analyzed.
5. The one-way coupled HH neuron system was simulated. The suitable noise would improve the efficiency of signal transmission. In addition, the noise and coupling coefficient of suitable intensity could make the system be in lag synchronization. The lag synchronization was redefined and analyzed according to the characteristics of stochastic system. In a one-way coupled system composed of 100 FN neurons, the lag synchronization was found, too. The self firing induced by strong coupling and the inhibition of firing induced by noise can be used to explain the corresponding phenomena of neuron.
6. The frequency sensitivity of the one way coupled HH neural system was investigated for the first time. The activities of the receptor changed with the variation of the parameters, i.e., the sensitive frequency changed with the noise and coupling. The transmission of multi-frequency signals was consistent with single-frequency signals. The noise was bad to the frequency sensitivity. The one way coupled neural net was alike a bandpass device. In addition, the one-way coupled net origins from central pattern generator, so the results can be used to explain the generating mechanism of its rhythm.
7. The effect of noise in the image processing of Pulse Coupled Neural Networks (PCNN) was simulated. It showed that noise could improve the results of image filtering and image enhancement. The PSNR and MSE of images also showed the existence of stochastic resonance. This study expands the fields of stochastic resonance, and is helpful to the study of image processing method.
本文的主要研究内容和成果为:
1、综合分析了近年来对脉冲发放神经元及其网络模型的研究,特别是其中的随机共振问题,对HH、FN神经元模型的放电特征和非线性动力学特征进行了研究。
2、在HH神经元随机模型中研究了噪声和高频信号的作用机制,强噪声导致的HH神经元长时放电,从模型角度解释了噪声引起耳鸣时听神经的自放电;噪声与高频的协作结果——高频信号对神经元放电有抑制,与生理实验结果一致,也表明神经系统中信号传输存在类似于听觉系统的双音遏制现象,即强度大的频率成分遏制强度低的频率成分;另外高频信号还导致神经元静息电位变为高频振荡,这些结果有助于开展神经系统的高频电磁场损伤治疗和防护研究。
3、对阈上单频和多频信号在HH神经元随机模型中的研究表明存在阈上随机共振现象,即适当强度的噪声同样有助于阈上信号的传输;神经元具有频率敏感性,类似于带通特性,且噪声强度可以改变神经元的敏感频率,即带通中心频率偏移,这些特点对于信号处理的研究具有重要意义。另外模型和结果与听觉系统的频率选择性特征相似,据此可以探讨听觉神经元频率选择的机制。
4、对阈下信号在FN神经元随机模型中的传输特性进行了研究和分析,结果不仅显示了随机共振的存在,还揭示FN神经元模型对正弦信号的传输与其频率密切相关,对频率处于0.2~0.8的正弦信号响应最强烈。此模型及结果可用于听神经纤维自发放电现象的解释。
5、HH单向耦合随机系统中的弱信号传输特性研究表明噪声通过随机共振使得系统实现了弱信号的检测和传输;适当的耦合强度和噪声强度可以实现神经滞后同步和最优的信息传递,并对此处的滞后同步进行了重定义和分析;在100个FN神经元构成的单向耦合随机系统中也发现了滞后同步的存在;另外模型仿真中出现的强耦合自放电及其被噪声抑制,有助于解释生物神经系统中神经元的自放电与其自我调制等现象。
6、首次对HH单向耦合随机系统的频率敏感性进行了分析,特别是接收元的行为,发现其敏感频率随噪声强度和耦合强度变化改变。多频叠加信号的结果与单频信号传输时一致,且噪声有碍于频率敏感性的表达。这些结果说明单向耦合系统也是一种带通器件,可通过改变自身的参数实现对某些频率的信号的最优传输。鉴于单向耦合网络源于中枢模式发生器,结果可用于解释它的节律发生机制。
7、首次通过PCNN随机模型研究了二维图像信号的处理中噪声扮演的角色,在高斯噪声图像滤波和低对比度图像的增强过程中均出现了随机共振现象,图像处理的效果得到了提高。因此拓展了随机共振的模型研究范围,有助于新的图像处理方法的研究。
With the development of physics, math, biology and computer, the investigation on brain has gained great achievements, especially the research on neural model. Scientists work on all kinds of neural models, trying to disclose the signal storing and processing of the brain, build brain model of cognition and realize the annual intelligence at last. Usually the scientific research begins from simple to complex, so the spiking neuron models and their coupled neural nets were selected as the main subject of this dissertation. Their nonlinear dynamic characteristics and signal transmission were studied. The role of noise was also discussed in the signal processing of the neuron models and net. The results show that noise is helpful to the signal processing through stochastic resonance. The characteristics of signal transmission were analyzed to reveal the neuron’s signal processing mechanism. These results are a kind of explanation of neural biological and physiological experiments in the models, are of significance to the experiments and treatments of some neural diseases.
The main contents and results of this thesis are as follows:
1. The studies on spiking neuron and net in recent years were reviewed, especially stochastic resonance in neural models. The firing characteristics and nonlinear dynamics of Hodgkin-Huxley (HH) and FitzHugh-Nagumo (FN) spiking neuron models were investigated.
2. The effects of high frequency (HF) signal on HH neuron stochastic model were studied. The HF signal inhibited the spiking of neuron, which was consistent with the physiological results. It was also similar with the two-tone suppression of auditory neuron. In addition, the HF signal could induce the resting potential change into high frequency oscillation. These results may be used to explain the corresponding physiological phenomenon.
3. The transmission of suprathreshold signal and multi- frequencies signals in the stochastic HH neuron model was investigated. Their transmission was influenced by noise through suprathreshold stochastic resonance. The model was of frequency sensitivity, similar to bandpass. It was alike the characteristics of auditory system, so it could be used to discuss the frequency selectivity of auditory neuron. The noise could change the sensitive frequency, i.e., the shift of center frequency of bandpass. It is of significance to signal processing method.
4. The transmission of subthreshold signal in FN stochastic model was investigated. The results showed that there was stochastic resonance and the transmission of sinusoidal signal was closely correlated with its frequency. The neuron model responded strongly with frequencies in the range of 0.2~0.8. Accordingly, the self firing activity of auditory neuron was analyzed.
5. The one-way coupled HH neuron system was simulated. The suitable noise would improve the efficiency of signal transmission. In addition, the noise and coupling coefficient of suitable intensity could make the system be in lag synchronization. The lag synchronization was redefined and analyzed according to the characteristics of stochastic system. In a one-way coupled system composed of 100 FN neurons, the lag synchronization was found, too. The self firing induced by strong coupling and the inhibition of firing induced by noise can be used to explain the corresponding phenomena of neuron.
6. The frequency sensitivity of the one way coupled HH neural system was investigated for the first time. The activities of the receptor changed with the variation of the parameters, i.e., the sensitive frequency changed with the noise and coupling. The transmission of multi-frequency signals was consistent with single-frequency signals. The noise was bad to the frequency sensitivity. The one way coupled neural net was alike a bandpass device. In addition, the one-way coupled net origins from central pattern generator, so the results can be used to explain the generating mechanism of its rhythm.
7. The effect of noise in the image processing of Pulse Coupled Neural Networks (PCNN) was simulated. It showed that noise could improve the results of image filtering and image enhancement. The PSNR and MSE of images also showed the existence of stochastic resonance. This study expands the fields of stochastic resonance, and is helpful to the study of image processing method.
引文
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