经验模式分解

经验模式分解

摘要

近些年来,随着计算机技术的高速发展与信号处理技术的不断提高,人们对图像的分析结构的要求也越来越高。目前图像处理已经发展出很多分支,包括图像分割、边缘检测、纹理分析、图像压缩等。经验模式分解(EMD)是希尔伯特-黄变换(Hilbert-HuangTransform)中的一部分,它是一种新的信号处理方法,并且在非线性、非平稳信号处理中取得了重大进步,表现出了强大的优势与独特的分析特点。该方法主要是将复杂的非平稳信号分解成若干不同尺度的单分量平稳信号与一个趋势残余项,所以具有自适应性、平稳化、局部性等优点。鉴于EMD方法在各领域的成功应用以及进一步的发展,国内外很多学者开始将其扩展到了二维信号分析领域中,并且也取得的一定的进展。但是由于二维信号不同于一种信号,限于信号的复杂性和二维数据的一些处理方法的有限性,二维经验模式分解(BEMD)在信号分析和处理精度上还存在一些问题,这也是本文要研究和改善的重点。

关键词：图像处理；信号分解；BEMD

In recent years, with the rapid development of computer technology and the continuous improvement of signal processing technology, the demand for the analysis structure of the image is becoming more and more high. At present, many branches have been developed in image processing, including image segmentation, edge detection, texture analysis, image compression and so on. Empirical mode decomposition (EMD) is a part of Hilbert Huang transform (Hilbert-HuangTransform). It is a new signal processing method, and has made significant progress in nonlinear and non-stationary signal processing, showing strong advantages and unique analysis points. This method mainly decomposes the complex non-stationary signals into several single scale stationary signals with different scales and a trend residual term, so it has the advantages of adaptability, stationarity and locality. In view of the successful application and further development of EMD method in many fields, many scholars at home and abroad have expanded it to the two-dimensional signal analysis field, and have made some progress. However, because two dimensional signal is different from one signal, it is limited to the complexity of signal and the processing methods of two-dimensional data. Two-dimensional empirical mode decomposition (BEMD) still has some problems in the accuracy of signal analysis and processing, which is also the important point of research and improvement in this paper.

Key words: image processing; signal decomposition; BEMD

摘要 (1)

第一章概况 (4)

2.EMD方法原理 (5)

2.1 本征模函数 (5)

2.2 .EMD分解过程 (5)

2.3.分解举例： (6)

3. BEMD分解原理 (8)

3.1 图像极值点的选取： (8)

3.2 Delaunay 三角剖分 (9)

3.3 基于三角网络的曲面插值 (11)

3.4 分解方法 (11)

3.5 BEMD 分解停止准则 (12)

4 二维经验模态分解在图像处理中的应用.................................... 错误!未定义书签。

4.1图像分解实例............................................................... 错误!未定义书签。

4.2图像降噪 ..................................................................... 错误!未定义书签。5总结...................................................................................... 错误!未定义书签。参考文献.................................................................................. 错误!未定义书签。