脉冲耦合神经网络关键特性的理论分析及应用研究
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摘要
脉冲耦合神经网络(PCNN, Pulse Coupled Neural Network)是一种有着生物学背景的新一代人工神经网络模型,它模拟了哺乳动物视觉皮层中神经元的信息处理机制。它在图像处理等领域得到了很好的运用,并显示了独特的优越性。然而,PCNN模型一直以来缺乏系统地理论分析,这使其在具体应用中面临神经元参数难以自动设定的问题。因此,本文对脉冲耦合神经网络的几个关键特性进行了深入地理论分析,并将其理论分析结果应用到了实际应用中。总的说来,本文所做研究工作的内容及进展主要在以下几个方面：
一、在PCNN和S-PCNN模型中,对神经元的动力学特性进行了定性的数学分析。在非外部脉冲耦合的自激励脉冲发放情形下,围绕神经元脉冲发放的周期和时间相位,给出了神经元自激励脉冲发放周期的数学描述；给出了PCNN神经元进入稳定自激励脉冲发放周期时的开始时间相位的数学描述；给出了S-PCNN神经元自激励脉冲发放时间相位的数学描述。在外部脉冲耦合情形下,给出了神经元的捕获期和不应期对应的数学描述。实验仿真验证了有关分析结论的正确性。
二、以动力学特性分析结果为基础,对神经元脉冲统计特性进行了分析,并将其理论成果应用于人脸识别和彩色图像增强。在理论分析中,围绕两种形式的脉冲统计方法：振荡时间序列OTS和脉冲振荡频图OFG,对OTS的不变性进行了分析,并从捕获特性角度将OTS分解为自激励OTS (S-OTS)和捕获性OTS (C-OTS);对OFG的区域特征聚类特性进行了分析,进而提出利用振荡频图序列OFGS来作为区域聚类演化的一种描述；给出了PCNN神经元参数的一种估计方法。在理论结果的应用中,利用PCNN提取的OTS特征实现了人脸识别；利用S-PCNN提取的OTS的分解特征X-OTS (OTS、 C-OTS和S-OTS)提出了一种人脸识别方法；基于S-PCNN和OFGS,结合高维空间中的矢量运算方法,提出了一种有效的彩色图像增强算法。实验仿真结果验证了相关应用的有效性。
三、以动力学特性分析结果为基础,对神经元脉冲同步振荡相关特性进行了分析,并将其理论成果应用于图像分割和椒盐噪声滤波。在理论分析中,给出了S-PCNN神经元产生同步振荡的必要条件,进而解释了PCNN神经元实现脉冲同步振荡的原因；对神经元脉冲同步振荡的时空相关性进行了分析；对利用神经元脉冲同步振荡的时间相位进行特征聚类的局限性进行了分析,进而分析了脉冲振荡频率进行特征聚类的合理性。在理论结果的应用中,利用PCNN神经元的脉冲振荡频率信息,提出了一种有效的图像分割方法,其中给出了一种神经元参数估计方法；利用S-PCNN神经元的脉冲同步振荡相关的原理实现了椒盐噪声的检测,其中给出了一种神经元的参数估计方法,同时针对噪声检测后的滤波需求,提出了扩展窗口中值滤波EWMF方法。实验仿真结果验证了相关应用的有效性。
四、以动力学特性分析的结果为基础,对神经元的脉冲波传播特性进行了分析,并将理论结果应用于多约束QoS路由求解。在理论分析中,给出了S-PCNN网络能形成脉冲波传播的环境条件和参数约束条件；然后根据参数约束条件的数学描述,实验分析了链接权和链接强度对脉冲波传播特性的影响。在理论结果的应用中,为了利用脉冲波传播来求解路由优化,提出了竞争型脉冲耦合神经网络CPCNN模型,并推导了该模型神经元参数的约束条件,进而基于脉冲波任务的产生、分解和状态转换理论,实现了多约束QOS路由问题的求解。实验仿真验证了相关应用的有效性。
Pulse Coupled Neural Network (PCNN) is a new generation of artificial neural network simulated the mechanism of information processing in the neurons of mammalian visual cortex. The PCNN has been successfully applied in image processing and other areas, and shows the unique superiority. However, the applications using PCNN always face the difficulty of neuron parameters estimation due to lack of fairly through theoretical analysis for PCNN. So this dissertation will theoretical analyze several characteristics for PCNN, and apply the analysis results to some practical applications. On the whole, the content and progress of the research work mainly in the following four aspects.
First, in the PCNN and the simplified PCNN (S-PCNN), the dynamic characteristics of neurons have been qualitatively analyzed. In a situation that a neuron without external coupling pulses firing self-stimulating pulses, the mathematical descriptions of the self-stimulating pulse period for PCNN and S-PCNN neurons, of the initial firing-pulse time phase in the state self-stimulating pulse period for PCNN neurons, and of the pulse time phase for S-PCNN neurons, have been obtained. On the other hand, in a situation that a neuron receives external coupling pulses, the mathematical descriptions of the captures-period and the refractory-period have been obtained. The experimental simulation to verify the correctness of the analysis conclusions.
Second, based on the analysis of the dynamic characteristics, analyzed the pulse statistical characteristics of neurons, and applied the theoretical analysis results to face recognition and color image enhancement. In the theoretical process, around two pulse statistical methods:Oscillation time sequences (OTS) and pulse oscillation frequency map (OFG), analyzed the invariance of the OTS, and divided the OTS into self-stimulating OTS (S-OTS) and captured OTS (C-OTS). Analyzed the clustering characteristics of regional features for the OFG, and using OFG sequences (OFGS) as a description of the evolution process of features clustering. Given a PCNN neuron parameters estimation method. In the practical applications, using the OTS in PCNN to realize face recognition, and using the X-OTS (OTS, C-OTS and S-OTS) in S-PCNN to realize face recognition. Based on S-PCNN and OFGS, combined with high-dimensional space vector operation, proposed an effective color image enhancement algorithms. Simulation results verify the validity of the applications.
Third, based on the analysis of the dynamic characteristics, analyzed the pulse oscillation correlative characteristics of neurons, and applied the theoretical analysis results to image segmentation and pulse noise filtering. In the theoretical process, given the necessary conditions of S-PCNN neurons firing synchronous pulses, and then obtained the causes of PCNN neuron realizing pulse synchronous oscillation. Analyzed the temporal correlations of neurons pulsing, and the limitation of using pulse oscillation time phase as the description feature clustering, and analyzed the reasonableness of using pulse oscillation frequency as the description of feature clustering. In the practical applications, based on the pulse oscillation frequency in PCNN, proposed an efficient image segmentation method with a neuron parameters estimation method. Used the synchronous pulse oscillation correlation in S-PCNN to realize impulse noise detection wih a neuron parameters estimation method and a filtering method called extended window median filter (EWMF). Simulation results verify the validity of the applications.
Fourth, based on the analysis of the dynamic characteristics, analyzed the pulse wave propagation characteristics of neurons, and applied the theoretical analysis results to multi-constrained QoS route problem. In the theoretical process, given the environment conditions and the parameters conditions constrained for occurring pulse wave propagation in S-PCNN, then based on the parameters condition constrained, using experimental methods to analyze the influences on pulse wave propagation characteristics for parameters. In the applications of the theoretical results, in order to solve route optimization using pulse wave propagation, proposed competitive pulse coupled neural network (CPCNN) model, and derived parameters condition constrained for neurons, and then combined with the theory of pulse task generation, decomposition and state transition, implemented the solution of multi-constrained QoS route problem. Simulation results verify the validity of the applications.
一、在PCNN和S-PCNN模型中,对神经元的动力学特性进行了定性的数学分析。在非外部脉冲耦合的自激励脉冲发放情形下,围绕神经元脉冲发放的周期和时间相位,给出了神经元自激励脉冲发放周期的数学描述；给出了PCNN神经元进入稳定自激励脉冲发放周期时的开始时间相位的数学描述；给出了S-PCNN神经元自激励脉冲发放时间相位的数学描述。在外部脉冲耦合情形下,给出了神经元的捕获期和不应期对应的数学描述。实验仿真验证了有关分析结论的正确性。
二、以动力学特性分析结果为基础,对神经元脉冲统计特性进行了分析,并将其理论成果应用于人脸识别和彩色图像增强。在理论分析中,围绕两种形式的脉冲统计方法：振荡时间序列OTS和脉冲振荡频图OFG,对OTS的不变性进行了分析,并从捕获特性角度将OTS分解为自激励OTS (S-OTS)和捕获性OTS (C-OTS);对OFG的区域特征聚类特性进行了分析,进而提出利用振荡频图序列OFGS来作为区域聚类演化的一种描述；给出了PCNN神经元参数的一种估计方法。在理论结果的应用中,利用PCNN提取的OTS特征实现了人脸识别；利用S-PCNN提取的OTS的分解特征X-OTS (OTS、 C-OTS和S-OTS)提出了一种人脸识别方法；基于S-PCNN和OFGS,结合高维空间中的矢量运算方法,提出了一种有效的彩色图像增强算法。实验仿真结果验证了相关应用的有效性。
三、以动力学特性分析结果为基础,对神经元脉冲同步振荡相关特性进行了分析,并将其理论成果应用于图像分割和椒盐噪声滤波。在理论分析中,给出了S-PCNN神经元产生同步振荡的必要条件,进而解释了PCNN神经元实现脉冲同步振荡的原因；对神经元脉冲同步振荡的时空相关性进行了分析；对利用神经元脉冲同步振荡的时间相位进行特征聚类的局限性进行了分析,进而分析了脉冲振荡频率进行特征聚类的合理性。在理论结果的应用中,利用PCNN神经元的脉冲振荡频率信息,提出了一种有效的图像分割方法,其中给出了一种神经元参数估计方法；利用S-PCNN神经元的脉冲同步振荡相关的原理实现了椒盐噪声的检测,其中给出了一种神经元的参数估计方法,同时针对噪声检测后的滤波需求,提出了扩展窗口中值滤波EWMF方法。实验仿真结果验证了相关应用的有效性。
四、以动力学特性分析的结果为基础,对神经元的脉冲波传播特性进行了分析,并将理论结果应用于多约束QoS路由求解。在理论分析中,给出了S-PCNN网络能形成脉冲波传播的环境条件和参数约束条件；然后根据参数约束条件的数学描述,实验分析了链接权和链接强度对脉冲波传播特性的影响。在理论结果的应用中,为了利用脉冲波传播来求解路由优化,提出了竞争型脉冲耦合神经网络CPCNN模型,并推导了该模型神经元参数的约束条件,进而基于脉冲波任务的产生、分解和状态转换理论,实现了多约束QOS路由问题的求解。实验仿真验证了相关应用的有效性。
Pulse Coupled Neural Network (PCNN) is a new generation of artificial neural network simulated the mechanism of information processing in the neurons of mammalian visual cortex. The PCNN has been successfully applied in image processing and other areas, and shows the unique superiority. However, the applications using PCNN always face the difficulty of neuron parameters estimation due to lack of fairly through theoretical analysis for PCNN. So this dissertation will theoretical analyze several characteristics for PCNN, and apply the analysis results to some practical applications. On the whole, the content and progress of the research work mainly in the following four aspects.
First, in the PCNN and the simplified PCNN (S-PCNN), the dynamic characteristics of neurons have been qualitatively analyzed. In a situation that a neuron without external coupling pulses firing self-stimulating pulses, the mathematical descriptions of the self-stimulating pulse period for PCNN and S-PCNN neurons, of the initial firing-pulse time phase in the state self-stimulating pulse period for PCNN neurons, and of the pulse time phase for S-PCNN neurons, have been obtained. On the other hand, in a situation that a neuron receives external coupling pulses, the mathematical descriptions of the captures-period and the refractory-period have been obtained. The experimental simulation to verify the correctness of the analysis conclusions.
Second, based on the analysis of the dynamic characteristics, analyzed the pulse statistical characteristics of neurons, and applied the theoretical analysis results to face recognition and color image enhancement. In the theoretical process, around two pulse statistical methods:Oscillation time sequences (OTS) and pulse oscillation frequency map (OFG), analyzed the invariance of the OTS, and divided the OTS into self-stimulating OTS (S-OTS) and captured OTS (C-OTS). Analyzed the clustering characteristics of regional features for the OFG, and using OFG sequences (OFGS) as a description of the evolution process of features clustering. Given a PCNN neuron parameters estimation method. In the practical applications, using the OTS in PCNN to realize face recognition, and using the X-OTS (OTS, C-OTS and S-OTS) in S-PCNN to realize face recognition. Based on S-PCNN and OFGS, combined with high-dimensional space vector operation, proposed an effective color image enhancement algorithms. Simulation results verify the validity of the applications.
Third, based on the analysis of the dynamic characteristics, analyzed the pulse oscillation correlative characteristics of neurons, and applied the theoretical analysis results to image segmentation and pulse noise filtering. In the theoretical process, given the necessary conditions of S-PCNN neurons firing synchronous pulses, and then obtained the causes of PCNN neuron realizing pulse synchronous oscillation. Analyzed the temporal correlations of neurons pulsing, and the limitation of using pulse oscillation time phase as the description feature clustering, and analyzed the reasonableness of using pulse oscillation frequency as the description of feature clustering. In the practical applications, based on the pulse oscillation frequency in PCNN, proposed an efficient image segmentation method with a neuron parameters estimation method. Used the synchronous pulse oscillation correlation in S-PCNN to realize impulse noise detection wih a neuron parameters estimation method and a filtering method called extended window median filter (EWMF). Simulation results verify the validity of the applications.
Fourth, based on the analysis of the dynamic characteristics, analyzed the pulse wave propagation characteristics of neurons, and applied the theoretical analysis results to multi-constrained QoS route problem. In the theoretical process, given the environment conditions and the parameters conditions constrained for occurring pulse wave propagation in S-PCNN, then based on the parameters condition constrained, using experimental methods to analyze the influences on pulse wave propagation characteristics for parameters. In the applications of the theoretical results, in order to solve route optimization using pulse wave propagation, proposed competitive pulse coupled neural network (CPCNN) model, and derived parameters condition constrained for neurons, and then combined with the theory of pulse task generation, decomposition and state transition, implemented the solution of multi-constrained QoS route problem. Simulation results verify the validity of the applications.
引文
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