自适应滤波器的设计与matlab的实现
摘要
本文从随机噪声的特性出发，分析了传统滤波和自适应滤波基本工作原理和性能，以及滤波技术的现状和发展前景。然后系统阐述了基本维纳滤波原理和自适应滤波器的基本结构模型，接着在此基础上结合最陡下降法引出LMS算法。在MSE准则下，设计了一个定长的自适应最小均方横向滤波器，并通过MATLAB编程实现。接着用图像复原来验证该滤波器的性能，结果表明图像的质量在MSE准则下得到了明显的改善。最后分析比较了自适应LMS滤波和频域维纳递归滤波之间的性能。本文还对MATLAB里面的自适应维纳滤波函数wiener2进行了简单分析。
关键字：退化图像 维纳滤波 自适应滤波 最陡下降法 LMS
Abstract
This paper analyses the basic work theory, performance of traditional filter and adaptive filter based on the property of random noise, and introduce the status quo and the foreground of filter technology. Then we explain basic theory of wiener filter and basic structure model of adaptive filter, and combine the method of steepest descent to deduce the LMS. Afterward according to the MSE rule, we design a limited length transversal filter, and implement by MATLAB. And then we validate performance of adaptive LMS filter by restoring images, Test result show that the quality of the degrade images were improved under the rule of MSE. Finally, we compare the performance of adaptive LMS filter and iterative wiener filter.We also simply analyses the wiener2 () which is a adaptive filter in MATLAB.
Keywords: degrade image；wiener filter；adaptive filter；ADF；LMS algorithm
1.1研究背景……………………………………………………………………………………………. 1
1.2研究目标及现状…………………………………………………………………………………. 1
1.2.1图像复原技术的目标…………………………………………………………. 1
1.2.2图像复原技术的研究现状………………………………………………….. 1
2.理论基础………………………………………………………………………………………………. 3
2.1基本自适应滤波器的模块结构……………………………………………………………. 3
2.2基本维纳滤波原理……………………………………………………………………………… 4
3 自适应滤波原理及算法………………………………………………………………………… 7
3.1 横向滤波结构的最陡下降算法…………………………………………………………… 7
3.1.1 最陡下降算法的原理………………………………………………………… 7
3.1.2 最陡下降算法稳定性………………………………………………………. 10
3.2 LMS滤波原理及算法…………………………………………………………………….. 12
3.2.1 从最陡下降法导出LMS算法………………………………………….. 12
3.2.2 基本LMS算法的实现步骤……………………………………………. 12
3.2.3 基本LMS算法的实现流程图………………………………………… 13
3.2.4 LMS算法的Matlab实现wiener2（）的原理………………….. 13
3.2.5 wiener2（）的原理………………………………………………………… 14
3.2.6 LMS性能分析——自适应收敛性…………………………………….. 15
4 Matlab实验结果……………………………………………………………………………….. 16
4.1 LMS滤波器的收敛性……………………………………………………………….. 16
4.2LMS滤波器和频域迭代维纳滤波器的性能比较…………………………………. 18
5总结……………………………………………………………………………………………………. 19
致 谢…………………………………………………………………………………………………… 21
参考文献……………………………………………………………………………………………….. 22
附录A…………………………………………………………………………………………………… 23
附录B…………………………………………………………………………………………………… 24
附录C…………………………………………………………………………………………………… 31
