小波分析在图像去噪中的应用

傅里叶分析与小波分析在图像去噪中的应用

Application of fourier analysis and wavelet analysis in image

denoising

总计毕业设计（论文） 3 9 页

表格 2 个

插图 1 1 幅

摘要

图像是人类传递信息的主要媒介。然而，图像在生成和传输的过程中会受到各种噪声的干扰，对信息的处理、传输和存储造成极大的影响。傅里叶变换是一种最常用最基本的频域分析法，能很好地刻画信号的频率特性，且不具有局部化特征。小波分析是局部化时频分析，它具有时域和频域联合表示信号的特征，通过伸缩、平移等运算功能对信号进行多尺度细化分析，能有效地从信号中提取信息，是分析非平稳信号的有力工具。

本文旨在研究傅里叶与小波理论去噪原理，首先简要概述傅里叶和小波在图像处理方面的发展现况；其次详细讨论了傅里叶和小波的基本理论，分别介绍了连续小波、离散小波、多分辨分析、二维小波分析。根据噪声一般是高频的特性，提出了通过傅里叶变换和低通滤波解决高频噪音的方法。因傅里叶去噪的局部局限性，在去噪的同时造成了图像的失真，结合小波时-频局部特征的能力，而提出了小波阈值去噪的方法，通过仿真实验结果分析，小波去噪能有效去除图像的高斯噪声，同时能很好的保留图像的细节信息，得到图像的最佳恢复。

关键词：傅里叶变换小波变换多分辨分析低通滤波阈值去噪

Abstract

The image is the main medium of the human convey information. However, there will be various noise in the process of image's generation and transmission, having great impact on the process of information processing and transmission. Fourier transform is one of the most commonly used and the most basic method of frequency domain, which can be very good to depict the frequency of the signal characteristics, and does not have localized features. Wavelet analysis is localized time-frequency analysis. It has the characteristics of the signal jointed by the time domain and frequency domain. Through expansion, the translation and etc of the arithmetic functions to carefully analysis the different scales signals, it can effectively extract information from the signal, and it is a powerful tool to analysis the non-stationary signals.

This paper aims to study fourier and wavelet denoising theory. Firstly, the paper briefly summarizes the developing condition of the principle of fourier transformation and wavelet transformation in image processing. Secondly, it discusses the basic theory of fourier transformation and wavelet transformation in detail, and respectively analysis’s continuous wavelet, discrete wavelet, multi-resolution analysis, two-dimensional wavelet. According to the characteristics of high frequency of noise, a method of solving high frequency noise has been put forward through the Fourier transform and low pass filter. Because of Fourier denoising local limitations in denoising which, at the same time, caused the distortions. But combined with wavelet time-frequency local characteristics, the method of wavelet threshold denoising has been put forward which through the simulation experiment result analysis of wavelet denoising ,can effectively remove the Gaussian noise image, and at the same time can well reserve the detail of the image information, getting the best image recovery .

Key words：Fourier transform; Wavelet Transform; Multiresolution analysis; Low-pass filter; Threshold denoising