基于改进阈值函数的小波去噪及其优化研究

发布时间：2018-01-10 20:17

本文关键词：基于改进阈值函数的小波去噪及其优化研究　出处：《昆明理工大学》2017年硕士论文　论文类型：学位论文

【摘要】：在计算机控制系统中,信号的传输、检测和采集等受到环境影响而遭到不同程度随机噪声污染,对此实行信号去噪十分必要。如何滤除实际信号中的噪声,并获取有用信号,是目前研究热点。特别是高频部分和强噪声相混叠信号、微弱信号或非平稳随机信号,传统处理平稳信号的傅里叶变换对这些信号不能局部分析,而小波变换拥有时频局部分析能力,对以上信号去噪效果相对较好,其应用也极为广泛。几类小波去噪方法里,小波阈值收缩去噪法可以在最小均方误差意义上接近最优,且拥有很好视觉成效,而受到及广的运用与深层次的研究。在小波阈值去噪方法里面,小波基、分解层数、阈值和阈值函数是小波阈值去噪的重要性因素。对各种含噪信号的处理,不一样的小波基具有着不一样的特点,可以十分确信的是:往往没有一种小波基函数能够针对所有类型的信号都获得最优的去噪效果。同时,对于分解层数来说,也可以十分确定的是:不相同的信号、不相同的信噪比下会对应着一种去噪效果较佳或接近最佳的分解层数。本文针对小波基函数和分解层数的确定创造出一个算法,能够针对待处理的信号做出分析,以信噪比为指标,算法通过计算采用不同的小波基函数或分解层数对待处理的含噪信号处理之后的信噪比改善量,得出其关系模型以确定最适当的小波基函数和分解层数。阈值函数的选取直接影响信号重构精确度,而对于先前的硬、软阈值函数拥有的一定缺点:硬阈值函数曲线在阈值处是不连续的,这种拥有间断点的现象会促使去噪之后重构信号更轻易发生附加的振荡,造成“伪吉布斯”现象,并且大于阈值的小波系数中也通常染杂着噪声的扰动,影响了最后重构信号的质量;软阈值函数也有自己的缺陷:在进行阈值处理时,当小波系数的绝对值大于或者等于此阈值时,直接采取了将小波系数都减去了阈值这个办法,这样会造成小波的估计系数和原来信号的小波系数两者具有一定的偏差,会很大程度上影响最后信号重构的效果。针对传统阈值函数的缺点,许多学者提出了在软、硬阈值中间的改进型阈值函数算法。但这些阈值函数在全部小波空间域内高阶不可导,拥有临界阈值处不能平滑过渡的现象。因此本文提出一个带参数的阈值函数,该阈值函数拥有更高阶,通过手动调节参数使之位于硬、软阈值函数中间,且同时拥有硬、软阈值函数的优点,并在临界阈值内添加平滑过渡区,可在阈值处理时保留一部分有用的高频信号,较好地抑制细节系数的“过扼杀”和信号振荡现象。并且通过实验进行仿真,仿真结果说明了本文提出的新阈值函数增大了信号的信噪比,降低了均方误差,获得了相对很好的去噪效果。采用带参数阈值函数去噪过程中,针对具体的含噪信号,可以灵活调节阈值函数的参数,满足不同信号处理的去噪要求。然而,在实际应用中,待处理信号的含噪情况是不可预测或不可知的。对于这种随机变化的含噪信号进行去噪,阈值函数的参数不应该也不可能是固定值。因此对于随机含噪信号的处理,选择适用的优化算法来对阈值函数的参数进行优化,以期能够适应信号的变化,这也是去噪走向实用化的关键。阈值函数有两个参数,函数优化时参数较少,同时对于变化信号的处理则需在较短时间内完成优化目标,因此,需要收敛速率相对较高的优化算法。通过对比模拟退火算法、遗传算法、神经网络算法、蚁群算法等优化算法,选取收敛速度快、精度高及易实现且无需过多参数调整的粒子群优化算法。采用粒子群优化算法,针对信号含噪情况,自动优化阈值函数参数,实现去噪过程的自动寻优。采用基准信号仿真结果表明,提出的算法可以获得更小的均方误差和更高的信噪比,具有去噪实用化的价值。
[Abstract]:In the computer control system, signal transmission, detection and acquisition are affected by environment and suffered different degrees of random noise pollution, regard the implementation of signal denoising is necessary. How to filter out the noise in the actual signal, and obtain the useful signal, is the current research focus. Especially high frequency and strong noise mixed signal, weak signal or non-stationary random signal, the Fu Liye transform of traditional processing non-stationary signals of these signals are not local analysis, and wavelet transform has the time-frequency analysis ability, the signal denoising effect is relatively good, its application is very extensive. Several kinds of wavelet denoising method, wavelet threshold denoising can be close to the optimal in minimum mean square error, and has a good visual effect, and is widely used and with deep research. Denoising method, wavelet threshold in wavelet decomposition, threshold The value and the threshold function is the important factor of wavelet threshold denoising. To deal with all kinds of noisy signal, wavelet basis is not the same with different characteristics, can be quite sure that is often not a wavelet function can denoising effect according to the signal of all types are optimal. At the same time, the decomposition the number, also can be determined is that the signal is not the same, not the same signal-to-noise will correspond to a decomposition denoising effect is better than or close to the best. Based on the wavelet function and decomposition level is determined to create an algorithm that can treat the signal needle to make analysis, the signal-to-noise ratio index by calculating wavelet decomposition level or different treated after the noisy signal processing improve SNR, the relation model to determine the most appropriate wavelet basis function And the decomposition level. Select the threshold function directly affects the accuracy of signal reconstruction, and for the previous hard, soft threshold function has some disadvantages: the hard threshold function is discontinuous on the threshold, this phenomenon will have discontinuous points after make denoising signal reconstruction are more likely to have additional oscillation caused by pseudo Gibbs "phenomenon, and greater than the wavelet coefficient threshold in noise disturbance usually contaminated, influence the quality of the final reconstructed signal; soft threshold function has its own drawbacks: the threshold processing, when the absolute value of wavelet coefficients greater than or equal to the threshold, the wavelet coefficients are directly taken by the threshold of this approach, the wavelet coefficients between the estimated coefficients which will cause the wavelet and the original signal has a certain deviation, will affect the final signal reconstruction greatly. According to the biography The threshold function defects, many scholars put forward the soft threshold function, the improved algorithm of hard threshold. But these intermediate threshold function in wavelet domain all high order non differentiable, with critical threshold can be a smooth transition phenomenon. Therefore this paper proposes a parameterized threshold function, the higher order has this threshold function, by manually adjusting the parameters so that at the middle of hard and soft threshold function, and also has the advantages of hard and soft threshold function, and add a smooth transition zone at a critical threshold, can keep part of the high frequency signal useful in threshold processing, restrain the detail coefficients of the "over kill" and the signal oscillation phenomenon. And through the simulation experiment, the simulation results show that the new threshold function is proposed to increase the signal-to-noise ratio, mean square error is reduced, to obtain a relatively good de-noising effect with ginseng The number of threshold function denoising process, the noisy signal is specific, can flexibly adjust the parameter of threshold function, meet the requirements of different denoising signal processing. However, in practical application, containing noise of the signal is unpredictable or unknown. For the random noise signal of denoising, threshold function parameters should not be fixed value. So for dealing with random noise signal, selection algorithm applicable to parameters of the threshold function is optimized, in order to adapt to the change of signal, which is the key to the practical denoising threshold function. There are two parameters. Function optimization and processing for signal changes less, is required to complete the optimization goal, within a short period of time, therefore, need to optimize the convergence rate is relatively high. By comparing the simulated annealing algorithm, genetic algorithm, neural Network algorithm, ant colony algorithm and other optimization algorithms, selection of fast convergence, high precision and easy realization of particle swarm optimization algorithm and without excessive parameter adjustment. Using particle swarm optimization algorithm for signal denoising, threshold function parameter optimization, realize the automatic optimization of the denoising process. The simulation results using the reference signal show that the mean square error of the proposed algorithm can get smaller and higher SNR with practical denoising value.

【学位授予单位】：昆明理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN911.7

【相似文献】