【作者】 葛洪伟；

【导师】 王士同；

【作者基本信息】 江南大学 ， 轻工信息技术与工程， 2008， 博士

【摘要】 基于可能性理论的可能性线性模型在模糊建模方面有着非常重要的作用,并已得到了广泛的研究。在使用可能性线性模型时,我们必须为模型选择一个自由参数h,即用于衡量拟合程度的门限阈值。该阈值选取得不好会严重影响模型的性能。在实际应用中,输入/输出数据经常含有噪声,如何选取合适的阈值参数,尤其是在噪声环境下,使可能性线性模型具有更好的噪声抑制能力,一直是一个悬而未决的问题,同时也是一个非常有趣和富有挑战性的理论课题。为了获得在输入样本含有噪声情况下合理选择可能性线性模型的拟合门限参数h的理论依据,本文深入研究了对称三角形模糊系数和非对称三角形模糊系数的可能性线性模型中的参数h与输入噪声之间的关系。文中,我们首先借鉴支撑向量回归(SVR)技术,将模型扩展为正则化的可能性线性模型,以提高其泛化能力,然后将其优化问题转换为最大后验估计(MAP)问题。借助于MAP框架,我们从理论上推导出了对称三角形模糊系数的可能性线性模型中的参数h与高斯噪声、拉斯噪声和均匀噪声的均方差之间的近似线性反比关系,也推导出了非对称三角形模糊系数的可能性线性模型的阈值参数与高斯输入噪声间的近似线性反比关系,而文中的多组仿真实验进一步证明了这些结论。显然,在实际应用中,这些结论对通常的可能性线性模型和正则化可能性线性模型的应用均有借鉴意义。中值滤波器是一种经典的非线性滤波器。该滤波器在有效抑制脉冲噪声的同时,会模糊信号的细节结构。为克服这一缺陷,我们基于上述的研究工作对中值滤波器进行改进,提出了一种基于正则化可能性线性模型的新型自适应滤波器。这种滤波器的输出是原始输入信号和经典中值滤波器的加权和,而权值则根据输入的信号序列由预先建好的可能性线性模型来决定。文中通过大量的比较实验说明,该滤波器在有效滤除脉冲噪声的同时能更好地保留图像的细节信息,且针对不同比例的脉冲噪声,表现出很好的鲁棒性。更多还原

【Abstract】 Possibilistic linear model based on possibility theory has a pivotal role in fuzzy modeling and has been widely studied. When adopting possibilistic linear model, one has to adopt an appropriate free parameter h, i.e. the threshold value used to measure degree of fit. A bad choice of the threshold value will severely deteriorate the performance of the model. In most practical situations, noise often appears in real input/output data. How to determine the appropriate threshold value, especially with the existence of noise, so as to improve the noise suppressing performance of possibilistic linear model, still keeps an open problem and is a very interesting but challenging theoretical issue at the same time.In order to determine the theoretically optimal choice of the threshold value h in possibilistic linear model with the existence of noisy input, the dependencies between parameter h and the input noise in possibilistic linear model using symmetric fuzzy triangular coefficients and non-symmetric fuzzy triangular coefficients are studied. In this paper, follow the spirit of support vector regression (SVR) techniques, we first extend possibilistic linear model to its regularized version, i.e. regularized possibilistic linear model, so as to enhance its generalization capability; The regularized model is then formulated as a corresponding equivalent maximum a posteriori (MAP) framework. With the help of the MAP framework, and after a series of mathematical derivation, the approximately inversely proportional dependency relationship that the parameter h in possibilistic linear model using symmetric fuzzy triangular coefficients with the standard deviation of Gaussion noisy input, Laplacian noisy input and Uniform noisy input should follow is derived respectively. And we also prove that with the existence of typical Gaussion noisy input, the free threshold of the model using non-symmetric fuzzy triangular coefficients is inversely proportional to Gaussion noisy input. At the same time, these theoretical claims are also confirmed by the simulation results. Obviously, these important conclusions are very helpful for the practical applications of both typical possibilistic linear model and regularized possibilistic linear model.Median filter is a typical non-linear filter and is well known for removing impulsive noises. But this filter distorts the fine structure of signals as well. In order to improve the performace of median filter, based on the reaserch work of possibilistic linear model, we propose a novel adaptive filter controlled by regularized possibilistic linear models. The proposed filter achieves its effect through a weighted summation of the input signal and the output of median filter, and the weights are set based on regularized possibilistic linear models concerning the states of the input signal sequence. The large amount results of compariton experimants in this paper show that this filter can preserve image details while effectively suppressing impulsive noises. Moreover, the new filter also provides excellent robustness with respect to various percentages of impulse noise in our testing examples.更多还原