神经元随机共振机制及其在语音与图像处理中的应用研究
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摘要
随机共振是非线性系统、随机噪声和输入信号之间的一种协同现象，它反映了噪声的积极作用，可以在很多非线性系统中观测到，特别是在神经系统中，随机共振发挥着重要的作用。
目前针对神经元模型的随机共振研究，主要集中于阈下单频周期信号输入的情况，但在现实中，非周期信号的检测和估计更具有实际应用意义，而且一些理论和模型研究表明，阈上信号情况下的随机共振可能是人类听觉和视觉感知的潜在机制。因此，论文重点围绕神经元模型的非周期阈上信号随机共振现象进行深入的研究，并基于阈上非周期随机共振机制，开展了语音复原、图像复原和图像增强的应用研究。
首先系统介绍了随机共振理论的发展、研究现状，简要说明了经典和非经典随机共振理论、各种计算模型，分析整理了常用的随机共振评价方法。
论文工作分三个部分：
1．关于神经元模型随机共振的研究选择了Hodgkin-Huxley(H-H)神经元模型、Fitzhugh-Nagumo神经元模型以及EEG模型，对随机共振在神经系统中信息处理的作用进行了仿真研究。在分析三种模型的阈下随机共振现象的基础上，重点研究了其阈上随机共振，采用信噪比、互相关系数、互信息率对比评价方法，定量描述神经元阈上随机共振现象的效果，分析神经元阈值特性，提供了随机共振机制在信息处理中的应用基础。实验结果表明：
神经元模型中的随机共振不仅仅局限于周期信号，对于非周期信号也广泛存在。这一结论揭示出生物体在复杂多变的环境中，可能利用随机共振机制达到微弱信号检测的目的。
在某些特定的条件下，神经元对阈上信号也能产生随机共振现象。
通过分析FHN神经元阈值特性，得出结论：神经元模型动力学行为可等效为两状态的阈值跨越行为。这是随机共振机制在信号检测和信息处理中的应用基础。
2．关于一维信息处理的应用研究
选择含噪语音信号作为研究对象，基于神经元阈上非周期随机共振机制，提出了一种随机共振语音复原算法，实现含噪语音信号阈上随机共振，从而达到语音复原的目的。利用改进后的互相关系数衡量语音信号的随机共振效果。将此方法对含噪语音信号的复原效果与传统方法复原效果做了比较和分析，得出结论：在强背景噪声情况下，本文方法的语音复原效果要优于传统方法。该方法具有一定的鲁棒性，有望转化为工程上的具体应用。
3．关于二维信息处理的应用研究
进一步分析图形图像类二维信号中随机共振的现象，提出一种自适应随机共振图像复原算法，并运用于灰度图像的复原处理。针对含噪彩色图像信息量较大、噪声寻优空间动态变化等特点，基于固定阈值、添加合适类型的噪声、采用折半方法快速寻找最佳噪声强度等方法，改进前述算法，提出一种快速自适应最优随机共振图像复原算法，并用于含噪灰度图像和彩色图像的复原处理。
定性与定量分析了图像复原系统中的阈上非周期随机共振现象，针对不同复原方法、不同噪声添加次数对复原效果的影响，进行了定性与定量的对比实验，实验结果表明，在二维信息处理中，无论对于含噪灰度图像还是彩色图像，在强背景噪声下，本文方法复原效果优于传统方法复原效果，算法鲁棒性较好，对于图像处理系统具有一定的通用性。
在算法改进过程中，对比分析了添加高斯白噪声和均匀分布随机噪声对随机共振效果以及图像复原效果的影响，实验结果表明，均匀分布随机噪声的性能优于高斯白噪声的性能。
最后，研究基于随机共振技术的微弱图像信号增强问题，即借助添加的噪声，将弱信号从图像中提取出来。
实验结果表明，相比于传统的图像增强方法，快速自适应随机共振图像增强算法可以借助添加的噪声能量，更好地提取出湮没在图像中的微弱信号，从而达到图像增强的目的。值得注意的是，该方法对RGB彩色模型和HSI彩色模型都具有一定的适用性，在某非零叠加噪声强度下，峰值信噪比均具有最大值，噪声的存在起到了改善图像质量的效果，但对不同的图像进行增强处理时，基于RGB模型和基于HSI模型的增强算法各具优势。
随机共振理论的应用研究并不局限于语音复原、图像复原、图像增强领域，在图像分割、机械故障检测等领域，也具有潜在的应用价值，需要在今后的工作中开展更广泛深入的研究和探索。
Stochastic resonance (SR) is a cooperative phenomenon between signal and randomnoise in the nonlinear system.It reflects whereby the noise can benefit to the signal,whichcan be observed in many nonlinear systems.Especially in the neural system,stochasticresonance may play an important role for information processing.
Up to now,the research of stochastic resonance in the neuron models was mainlyfocused on the subthreshold periodic input.But indeed,application of SR techniques toaperiodic signal detection or estimation is more meaningful.Furthermore,Some researches oftheory and models indicate that suprathreshold stochastic resonance may be the mechanismof human hearing and visual signal detection.This thesis focused on the research ofsuprathreshold aperiodic stochastic resonance in neuron models,and this mechanism to detectweak signal was applied to speech restoration,image restoration and image enhancement.
At first,the research status of the SR theory was introduced.The traditional andnon-traditional SR theory was explained in brief,and the formal methods for performanceevaluation of stochastic resonance were analyzed.
The work of the thesis includes three parts.
1.Research of stochastic resonance in the neuron models
The function of the stochastic resonance for information processing in neural systemwas simulated by using of Hodgkin-Huxley (H-H) neuron model,Fitzhugh-Nagumo(FHN)neuron model and EEG model.Based on analyzing the subthreshold SR phenomenon,thesuprathreshold SR was studied carefully.The effect of suprathreshold stochastic resonance ofthe neuron models was analyzed quantitatively by signal-noise-ratio,cross correlationcoefficient and mutual information ratio.The threshold characteristic of one neuron wasdiscussed.The result of simulation and experiment showed that in follows:
Stochastic resonance in the neuron models was not only for periodic signal but alsofor aperiodic signal.It revealed that the organism may make use of stochasticresonance to detect the weak signal in complex background.
Suprathreshold SR would be happened in the neuron models under certainconditions.
By analyzing the threshold characteristic of FHN neuron,the conclusion wasobtained that the dynamics conduct can be equivalent to the transit action from onestate to another.
2.Study of application on one-dimension signal processing
The corrupted speech signal was selected as a case study.The SR performance of speechsignal was estimated by the improved cross correlation coefficient.The speech restorationalgorithm was proposed based on the mechanism of suprathreshold stochastic resonance inthe neuron models,and was used to reconstruct the speech signal.Compared with traditionalrestoration methods,this new method had better performance and good robustness.
3.Study of application on two-dimension signal processing
The stochastic resonance phenomenon in two-dimension image signals was analyzed.Self-adaptive stochastic resonance method of image restoration was proposed and used torestore gray-scale image with noise.Because the information amount of the color image withnoise was very large and the range of optimum noise intensity was variable,fast self-adaptiveoptimal stochastic resonance method of image restoration was proposed and used to restoregray-scale image and color image with noise.The new method was based on thefixed-threshold and the certain type of noise.The quick-bisearch method was designed toimprove the efficiency of algorithm.
The phenomenon of suprathreshold aperiodic stochastic resonance was analyzedquantitatively and qualitatively.The contrast experiments were done according to variousrestoration methods and various adding noise number.In two-dimension informationprocessing,the restoration performance and robustness of gray-scale image or color imagewith noise were both better than the formal methods'.
Comparing the effect of equality distributing stochastic noise and Gaussian white noiseto the stochastic resonance performance and image restoration quality,it was found that thecharacteristic of the equality distributing stochastic noise was better than of Gaussian whitenoise.
At last,the question of the enhancement of weak image signal was studied based SRmechanism in order to detect the weak signal from the image with the help of the addednoise.
The experiment results showed that the fast self-adaptive stochastic resonance methodwas effective to enhance the image.It was remarkable that the method based on RGB colormodel and the method based on HSI color model has some advantage respectively.
The SR theory can be used in many other fields,such as image segment,test ofmechanical failure,etc.It is valuable to study more deeply and widely.
目前针对神经元模型的随机共振研究，主要集中于阈下单频周期信号输入的情况，但在现实中，非周期信号的检测和估计更具有实际应用意义，而且一些理论和模型研究表明，阈上信号情况下的随机共振可能是人类听觉和视觉感知的潜在机制。因此，论文重点围绕神经元模型的非周期阈上信号随机共振现象进行深入的研究，并基于阈上非周期随机共振机制，开展了语音复原、图像复原和图像增强的应用研究。
首先系统介绍了随机共振理论的发展、研究现状，简要说明了经典和非经典随机共振理论、各种计算模型，分析整理了常用的随机共振评价方法。
论文工作分三个部分：
1．关于神经元模型随机共振的研究选择了Hodgkin-Huxley(H-H)神经元模型、Fitzhugh-Nagumo神经元模型以及EEG模型，对随机共振在神经系统中信息处理的作用进行了仿真研究。在分析三种模型的阈下随机共振现象的基础上，重点研究了其阈上随机共振，采用信噪比、互相关系数、互信息率对比评价方法，定量描述神经元阈上随机共振现象的效果，分析神经元阈值特性，提供了随机共振机制在信息处理中的应用基础。实验结果表明：
神经元模型中的随机共振不仅仅局限于周期信号，对于非周期信号也广泛存在。这一结论揭示出生物体在复杂多变的环境中，可能利用随机共振机制达到微弱信号检测的目的。
在某些特定的条件下，神经元对阈上信号也能产生随机共振现象。
通过分析FHN神经元阈值特性，得出结论：神经元模型动力学行为可等效为两状态的阈值跨越行为。这是随机共振机制在信号检测和信息处理中的应用基础。
2．关于一维信息处理的应用研究
选择含噪语音信号作为研究对象，基于神经元阈上非周期随机共振机制，提出了一种随机共振语音复原算法，实现含噪语音信号阈上随机共振，从而达到语音复原的目的。利用改进后的互相关系数衡量语音信号的随机共振效果。将此方法对含噪语音信号的复原效果与传统方法复原效果做了比较和分析，得出结论：在强背景噪声情况下，本文方法的语音复原效果要优于传统方法。该方法具有一定的鲁棒性，有望转化为工程上的具体应用。
3．关于二维信息处理的应用研究
进一步分析图形图像类二维信号中随机共振的现象，提出一种自适应随机共振图像复原算法，并运用于灰度图像的复原处理。针对含噪彩色图像信息量较大、噪声寻优空间动态变化等特点，基于固定阈值、添加合适类型的噪声、采用折半方法快速寻找最佳噪声强度等方法，改进前述算法，提出一种快速自适应最优随机共振图像复原算法，并用于含噪灰度图像和彩色图像的复原处理。
定性与定量分析了图像复原系统中的阈上非周期随机共振现象，针对不同复原方法、不同噪声添加次数对复原效果的影响，进行了定性与定量的对比实验，实验结果表明，在二维信息处理中，无论对于含噪灰度图像还是彩色图像，在强背景噪声下，本文方法复原效果优于传统方法复原效果，算法鲁棒性较好，对于图像处理系统具有一定的通用性。
在算法改进过程中，对比分析了添加高斯白噪声和均匀分布随机噪声对随机共振效果以及图像复原效果的影响，实验结果表明，均匀分布随机噪声的性能优于高斯白噪声的性能。
最后，研究基于随机共振技术的微弱图像信号增强问题，即借助添加的噪声，将弱信号从图像中提取出来。
实验结果表明，相比于传统的图像增强方法，快速自适应随机共振图像增强算法可以借助添加的噪声能量，更好地提取出湮没在图像中的微弱信号，从而达到图像增强的目的。值得注意的是，该方法对RGB彩色模型和HSI彩色模型都具有一定的适用性，在某非零叠加噪声强度下，峰值信噪比均具有最大值，噪声的存在起到了改善图像质量的效果，但对不同的图像进行增强处理时，基于RGB模型和基于HSI模型的增强算法各具优势。
随机共振理论的应用研究并不局限于语音复原、图像复原、图像增强领域，在图像分割、机械故障检测等领域，也具有潜在的应用价值，需要在今后的工作中开展更广泛深入的研究和探索。
Stochastic resonance (SR) is a cooperative phenomenon between signal and randomnoise in the nonlinear system.It reflects whereby the noise can benefit to the signal,whichcan be observed in many nonlinear systems.Especially in the neural system,stochasticresonance may play an important role for information processing.
Up to now,the research of stochastic resonance in the neuron models was mainlyfocused on the subthreshold periodic input.But indeed,application of SR techniques toaperiodic signal detection or estimation is more meaningful.Furthermore,Some researches oftheory and models indicate that suprathreshold stochastic resonance may be the mechanismof human hearing and visual signal detection.This thesis focused on the research ofsuprathreshold aperiodic stochastic resonance in neuron models,and this mechanism to detectweak signal was applied to speech restoration,image restoration and image enhancement.
At first,the research status of the SR theory was introduced.The traditional andnon-traditional SR theory was explained in brief,and the formal methods for performanceevaluation of stochastic resonance were analyzed.
The work of the thesis includes three parts.
1.Research of stochastic resonance in the neuron models
The function of the stochastic resonance for information processing in neural systemwas simulated by using of Hodgkin-Huxley (H-H) neuron model,Fitzhugh-Nagumo(FHN)neuron model and EEG model.Based on analyzing the subthreshold SR phenomenon,thesuprathreshold SR was studied carefully.The effect of suprathreshold stochastic resonance ofthe neuron models was analyzed quantitatively by signal-noise-ratio,cross correlationcoefficient and mutual information ratio.The threshold characteristic of one neuron wasdiscussed.The result of simulation and experiment showed that in follows:
Stochastic resonance in the neuron models was not only for periodic signal but alsofor aperiodic signal.It revealed that the organism may make use of stochasticresonance to detect the weak signal in complex background.
Suprathreshold SR would be happened in the neuron models under certainconditions.
By analyzing the threshold characteristic of FHN neuron,the conclusion wasobtained that the dynamics conduct can be equivalent to the transit action from onestate to another.
2.Study of application on one-dimension signal processing
The corrupted speech signal was selected as a case study.The SR performance of speechsignal was estimated by the improved cross correlation coefficient.The speech restorationalgorithm was proposed based on the mechanism of suprathreshold stochastic resonance inthe neuron models,and was used to reconstruct the speech signal.Compared with traditionalrestoration methods,this new method had better performance and good robustness.
3.Study of application on two-dimension signal processing
The stochastic resonance phenomenon in two-dimension image signals was analyzed.Self-adaptive stochastic resonance method of image restoration was proposed and used torestore gray-scale image with noise.Because the information amount of the color image withnoise was very large and the range of optimum noise intensity was variable,fast self-adaptiveoptimal stochastic resonance method of image restoration was proposed and used to restoregray-scale image and color image with noise.The new method was based on thefixed-threshold and the certain type of noise.The quick-bisearch method was designed toimprove the efficiency of algorithm.
The phenomenon of suprathreshold aperiodic stochastic resonance was analyzedquantitatively and qualitatively.The contrast experiments were done according to variousrestoration methods and various adding noise number.In two-dimension informationprocessing,the restoration performance and robustness of gray-scale image or color imagewith noise were both better than the formal methods'.
Comparing the effect of equality distributing stochastic noise and Gaussian white noiseto the stochastic resonance performance and image restoration quality,it was found that thecharacteristic of the equality distributing stochastic noise was better than of Gaussian whitenoise.
At last,the question of the enhancement of weak image signal was studied based SRmechanism in order to detect the weak signal from the image with the help of the addednoise.
The experiment results showed that the fast self-adaptive stochastic resonance methodwas effective to enhance the image.It was remarkable that the method based on RGB colormodel and the method based on HSI color model has some advantage respectively.
The SR theory can be used in many other fields,such as image segment,test ofmechanical failure,etc.It is valuable to study more deeply and widely.
引文
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