基于微分算子的零空间追踪算法及其在生理信号处理中的应用

发布时间：2018-04-18 12:57

本文选题：信号处理 + 零空间追踪算法　；参考：《北方工业大学》2017年硕士论文

【摘要】：随着计算机和电子信息技术的迅速发展,数字信号处理技术的理论、算法以及实现手段也越来越多的被人们所关注。在这其中,信号的模型表示和信号分解是我们最想研究的方向。许多学者在这一研究领域提出了很多方法,把一个信号分解为几个信号的和的形式就是信号分解,即信号的模型表示。本文中的基于微分算子的零空间追踪算法,就是一种很好的信号分解算法。基于微分算子的零空间追踪(NSP)算法在信号去噪和信号分解中有着广泛的应用。该算法是彭思龙教授和黄文良教授在2008年的时候提出的一种全新的自适应信号分解算法。它不同于其他的分解方法,该算法定义了一种微分算子,使得分解出的信号在我们所定义的微分算子的零空间中。由于不同类型的信号会属于不同阶数的微分算子的零空间中,为了使可以分解的信号范围更加广泛,胡晰远博士在2011扩展了零空间追踪算法。在此之后,又有许多研究人员提出了不同类型的微分算子,进而对该算法进行了改进,提高了可分解信号的范围。本文中,我们将偶数阶微分算子应用到零空间追踪算法中,依据输入信号的特点,确定微分算子的阶数,再通过求解最优化问题,估算出微分算子的系数,从而确定微分算子的形式,即确定了有哪些提取信号属于该算子的零空间。最后,我们举例证实了该算法的可行性。在本文的第三部分中,我们首先利用零空间追踪算法对实际生理信号脑电波进行了去噪处理。然后我们对专家的分类结果进行分析,从信号的频率和信号的数值分布特点两方面给出睡眠期分类的方法,从中找到了一个分类标准,使得该分类标准可以应用于任何脑波数据。实验证明了我们的分类结果和专家的分类结果吻合度达到了百分之八十,可以看出,我们的睡眠分类标准还是比较不错的。
[Abstract]:With the rapid development of computer and electronic information technology, more and more attention has been paid to the theory, algorithm and realization of digital signal processing technology.Among them, the signal model representation and signal decomposition are the most desired research direction.Many scholars have put forward a lot of methods in this field. The form of decomposing a signal into the sum of several signals is signal decomposition, that is, the model representation of signal.The zero space tracking algorithm based on differential operator in this paper is a good signal decomposition algorithm.The zero space tracking (NSP) algorithm based on differential operators is widely used in signal denoising and signal decomposition.This algorithm is a new adaptive signal decomposition algorithm proposed by Professor Peng Sloan and Professor Huang Wenliang in 2008.It is different from other decomposition methods. This algorithm defines a differential operator so that the decomposed signal is in the zero space of the differential operator we define.Because different types of signals belong to the zero space of differential operators of different orders, in order to make the range of decomposable signals more extensive, Dr. Hu extended the null space tracking algorithm in 2011.After that, many researchers proposed different types of differential operators, and then improved the algorithm to increase the range of decomposable signals.In this paper, we apply the even-order differential operator to the zero-space tracking algorithm, determine the order of the differential operator according to the characteristics of the input signal, and then estimate the coefficient of the differential operator by solving the optimization problem.Thus, the form of differential operator is determined, that is, which extracted signals belong to the null space of the operator.Finally, we illustrate the feasibility of the algorithm.In the third part of this paper, we first use the zero-space tracking algorithm to de-noise the actual physiological signal brain waves.Then we analyze the classification results of the experts, and give a classification method of sleep period from two aspects: the frequency of the signal and the numerical distribution of the signal, and find a classification standard.So that the classification criteria can be applied to any brain wave data.The experimental results show that the degree of agreement between our classification results and expert classification results is up to 80%. It can be seen that our sleep classification criteria are quite good.
【学位授予单位】：北方工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.3;TN911.7

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