【作者】 邸飚；

【导师】 GAO Xi-qi； HU Ke-qin；

【作者基本信息】 东南大学 ， 电子与信息工程， 2005， 硕士

【摘要】 小波变换不仅在数学上已形成一个新分支，而且在应用上，如信号处理、图象处理、模式识别、量子物理以及众多非线性科学领域，被认为是近年来在分析工具及方法上的重大突破。本论文开展小波变换及其在图象解噪和压缩编码中的应用的研究。 本论文共分六章。第一章给出了论文的研究背景和意义。第二章详细阐述了小波变换理论。文中将傅里叶变换、Gabor变换和小波变换进行了对比分析，详细地讨论了高斯函数的性质和Gabor变换的性质。第三章以正交小波和双正交小波这两类小波为例讨论了尺度函数和小波函数在时间域和频率域满足的双尺度方程和边界条件以及滤波器系数所满足的关系式。Mallat算法是实现小波分解和重构的重要算法，文中详细地给出了其实现过程和原理，讨论了小波基的选取原则，分析了影响小波基压缩性能的影响因素—正则性和消失矩。第四章详细论述了小波阈值降噪的理论、方法。用MATLAB语言实现了基于BAYES式的图像降噪、基于像素背景的图像降噪以及基于最短描述长度原则的图像降噪与压缩。第五章介绍了图象压缩的几类方法，详细描述并实现了零树算法。第六章对全文进行了总结。更多还原

【Abstract】 Wavelet transform has been looked as a powerful analytic tool and method. It becomes more and more important not only in the theory field—mathematical in which it has built a new division but also in more application fields—signal processing, image processing, model distinguishing, quantum physics and more non-linear processing. This dissertation focuses on the research of wavelet transform and the applications of image de-noise and compress.This dissertation is divided into six chapters. Chapter 1 introduces research background and main work of this paper. Chapter 2 describes the wavelet transform theory in details. In this chapter, three kinds of signal transform methods were compared: Fourier Transform, Gabor Transform and Wavelet Transform. And the property of Guassian Function and Gabor Transform were shown in details. In chapter 3, some important properties of wavelet transform were investigated. Two main kinds of wavelet: orthogonal wavelet and bi-orthogonal wavelet, are used to show the performances of scales function and wavelet function in the time-domain and frequency-domain. Chapter 4 introduces the theory and methods of threshold de-noising in wavelet domain. And in this chapter, some newmethods—Bayes shrink, MDLQ threshold and Context Threshold are shown in details,followed by they were simulated with the computer based on the Matlab. Chapter 5 introduces some compress methods. And the Zerotree method is simulated. Conclusions are drawn in Chapter 6. Some further research on wavelet transform threshold de-noising and compress are also discussed.更多还原