【作者】 孙轶；

【导师】 张培仁；

【作者基本信息】 中国科学技术大学 ， 模式识别与智能系统， 2008， 博士

【摘要】 由于现实中的信号都是含噪信号,干扰噪声信号会导致原始信号发生畸变,甚至面目全非,因此如何从含噪信号中恢复原始信号实现信噪分离,提高信号的信噪比成为一项重要的研究课题。本文深入研究了对含噪信号进行去噪所涉及的问题,并提出如下三种基于提升小波变换的信号去噪方法:首先,传统的小波变换方法用于信号去噪存在这样几个缺点:现实中的信号是多样的,传统的单一小波变换无法满足信号多样性的要求;传统小波变换在自身构造以及对信号进行时-频-时变换需要耗费大量的系统资源。针对上述问题,本文提出一种基于Laurent多项式欧几里德算法的提升小波变换方法来构造正交小波库,能够根据采样信号的特征自适应选取合适的小波,并将其应用到信号去噪中。该方法有如下特点:构造的小波库满足了信号多样性的要求;提升方法构造的小波变换仅在时域对信号进行分析,大大减少了计算量;基于提升方法构造有着良好的灵活性、实时性和自适应性。其次,典型的提升方法将信号处理过程分为三个阶段:分解、预测和更新。原有的自适应预测方法是推导出多项式预测算子中的设计参数,通过自适应算法得出该参数,该方法把算子参数设计与自适应算法完全分离,彼此相互独立。在这种条件下,本文的卡尔曼自适应预测算法表现出了良好的实时性和灵活性。卡尔曼预测算法在对信号预测的过程中能够自适应地调整增益矩阵参数,使得被预测误差满足最小均方误差准则,此方法将预测与自适应有机的结合在一起,也大大减少了实时分析信号过程中的运算量。最后,在自适应预测的基础上,本文提出一种双自适应提升方法,即在提升过程中采用自适应的方法设计更新算子和预测算子。原有的自适应提升方法是先预测后更新的方法,当预测算子为空间变化或者非线性算子时,这种非线性因素会传递到更新算子当中,从而影响更新算法的性能。因此本文采用先更新后预测的方法,可以有效的避免由于预测算法的非线性因素导致更新算法的不准确。采用先更新后预测的方法,处理后信号的信噪比有所提高。原有的阈值去噪方法有各自的特点:硬阈值函数能够很好的保留信号边缘的局部特征,对突变信号的消噪效果比较好;软阈值函数则比较平滑,但是容易造成信号边缘模糊等失真现象。为了兼顾软阈值和硬阈值方法各自的优点,本文提出一种半软阈值去噪方法,半软阈值函数在噪声和信号之间存在一个平滑过渡的区域,使其更加符合自然信号或者图像的连续性。本文的仿真和实验表明了上述方法的有效性。更多还原

【Abstract】 In the real world all of the signals are noisy signals, and noise interference will result in the distortion or even thorough change in the original signal, so it becomes an important research subject that how to restore the original signal from the noisy signal so as to realize the isolation of signals and noises and se the letter and improve signal to noise ratio become improve the SNR. In this paper, in-depth study is performed regarding the issues involved in the denoising of noisy signals, and make several denoising methods based on lifting wavelet transform are raised. Below are the three signal denoising methods raised in this paper.There are several shortcomings of the traditional wavelet transform method for signal denoising: on the one hand, the signal is various, and the traditional single wavelet transform cannot meet the needs of signal diversity; on the other hand, it consumes a significant amount of system resources for traditional wavelet transform to perform time-frequency-time change on signals, considering its own structure. To address the above issues, the paper proposes a method based on adaptive lifting wavelet transform to conformation orthonormal wavelets libraries. This method could select the appropriate wavelet according to the characteristics of sampling signals, and apply it to signal denoising. The method has quite a few features: the wavelet libraries conformed meet the requirement of signal diversity; the wavelet transform conformed based on adaptive lifting performs analysis of signals only on time-domain signal, which decreases the computation substantially; the conformation based on adaptive lifting has excellent representation in enhancing flexibility, real-time and adaptability.The typical lifting method divides the signal process into three stages: decomposition, forecasts and updates. In the original forecast is to calculate the design parameter in the operator by deriving polynomial. The parameter is obtained through adaptive algorithm. The method separates the operator parameter design and adaptive algorithm completely, and make them independent with each other. In such conditions, Kalman adaptive forecast algorithm, put forward in the article, represents good flexibility and simple operation. Kalman forecast algorithm could adjust parameter adaptively in the process of signal forecast to gain matrix parameters, making the prediction error meet the Minimum Mean Square Error Approach (MMSE). This method combines forecast and adaptivity organically, and reduces the computation significantly in the process of real-time signal analysis.There are different characteristics of the original threshold denoising method. Hard-threshold function has good performance in retaining the partial features of signal edge and in denoising mutant signals. Soft-threshold function is more smooth, however could lead to distortion such as vague signal edge. To balance the strength of hard-threshold and soft-threshold, the paper raises a half soft-threshold denoising method. For half soft-threshold function, there is a smooth transition area between noises and signals, which make it more coincident in continuity of natural signals or images.The simulations and experiments in the paper have indicated the effectiveness of the above methods.更多还原