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< /p>

-

黄变换

(Hilbert-Huang Transform)

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；< /p>

BEMD

Abstract

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

目

录

摘

要

............... .................................................. ..............................................

1

第一章

概况

.

.. .................................................. ..................................................

4

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

.