摘 要

随着计算机性能的不断提高，数字图像处理学科也在不断的发展，近年来，Emmanuel J.Candes和 David L.Donoho提出的Curvelet变换引起了有关研究人员的密切关注，它被认为在图像处理领域即将成为一项新技术。Curvelet变换是由小波变换和脊波变换发展起来的，它克服了小波变换在应用中的不足。小波分析理论是由傅里叶分析发展而来的。小波变换能有效处理非平稳信号，与傅立叶分析相比，它能更“稀疏”地表示一维分段光滑或者有界变差函数。但是，小波分析的优异特性并不能推广到高维。Curvelet变换是一种新的多尺度分析的方法，比小波更加适合分析二维图像中的曲线或直线状边缘特征，而且具有更高的逼近精度和更好的稀疏表达能力。第二代的Curvelet变换是比第一代Curvelet变换更加快速简便的另一种变换，它省略了第一代Curvelet变换中子带分解、平滑分块、重正规化、脊波分解、脊波合成等一系列繁琐的步骤。

本文将介绍第二代Curvelet变换在图像融合、图像去噪、图像增强等几个方面的应用。本文主要基于第二代Curvelet变换实现了图像的融合。通过实验首先得到了经过第二代Curvelet变换后的图像的系数矩阵，经实验分析得出，图像被分解成Coarse层、Detail层和Fine层，Coarse尺度层由低频系数系数构成，Fine尺度层由高频系数构成。本文还通过对图像分别采用三层、四层和五层Curvelet变换进行了图像融合，比较了它们的熵值、灰度标准差、灰度均值和清晰度，得出四层Curvelet变换的图像融合效果是最佳的。在进行图像融合时，本文采用了高低频系数互补、低频系数加权、高频系数加权以及高低频系数都加权的方法进行了图像融合，对融合后图像的熵值、灰度标准差、灰度均值及清晰度进行了分析比较，得出高低频系数互补的融合方法较好。本文还实现了基于第二代Curvelet变换的图像去噪，通过对原始图像加噪然后再去噪，看出图像去噪的效果是比较理想的。

关键词：Curvelet变换；小波变换；图像融合；图像去噪；图像增强

Abstract

With the increasing performance of computer hardware and software, digital image processing has also been the development of disciplines in recent years, Emmanuel J. Candes and David L. Donoho's Curvelet transform the study attracted the close attention of staff, particularly in the field of image processing , it is considered will be a very useful new technology. Curvelet transform in the wavelet transform and wavelet transform ridge developed on the basis of its wavelet transform to overcome the deficiencies in the application, showing its own advantage. Wavelet analysis and Fourier analysis method is evolved. Wavelet transform is a powerful non-stationary signal processing tools, Fourier analysis can be more than "sparse" in that one-dimensional piecewise smooth or bounded variation function, which is the field of wavelet analysis in many disciplines with great success in one of the key reasons . However, in the one-dimensional wavelet analysis has excellent properties when they can not simply be extended to two or higher dimensions. Curvelet transform as a new multi-scale wavelet analysis method is more suitable than the two-dimensional image of the curve or line-like edge features, but also has higher accuracy and better sparse approximation expression. Curvelet transform is a second generation of faster and easier than Curvelet transform another transformation, it omitted the first generation of neutrons with Curvelet transform decomposition, smooth block, heavy regularization, ridge wave decomposition, synthesis and a series of complicated ridgelet steps.

This article will introduce the second generation Curvelet transform in image fusion, image denoising, image enhancement, and several other aspects of the application, and to explore the development trend and some of it needs further study. This article is based on second-generation Curvelet transform the image fusion. After the experiment was the first second-generation image Curvelet transformed coefficient matrix, obtained by experimental analysis, the image is broken down into Coarse layer, Detail level layer and Fine, Coarse-scale low-frequency coefficients by the coefficient of layer composition, Fine-scale layer consists of constitute a high-frequency coefficients. This article also were used by the image three, four and five Curvelet transform the image fusion, compared to their entropy, gray standard deviation, mean and clarity come to four Curvelet transform image fusion effect is the best. When carrying out fusion, we use high-frequency coefficients of complementary, low-frequency coefficient weighted, high-frequency coefficients and high frequency coefficients are weighted means were weighted image fusion, the fused image entropy, standard deviation of gray, gray Mean and clarity are analyzed and compared, the high frequency coefficients obtained fusion method can complement each other. The article also implemented based on the second generation Curvelet transform denoising, the original image by adding noise and then noise again, to see the effect of image denoising is ideal.

Key words: Curvelet transform; wavelet transform; image fusion; image denoising; image enhancement

目录

摘要 2

Abstract 3

目录 5

第一章 绪论 7

1.1 图像处理 7

1.2 Curvelet变换背景 7

1.3 Curvelet变换的研究现状 8

1.4 本文研究内容 9

1.5 本文章节安排 10

第二章 曲波理论 11

2.1小波变换 11

2.2 多尺度几何分析 11

2.3 脊波变换 12

2.4 Curvelet变换 13

2.5 基于Curvelet变换图像分解 16

2.6 小波变换与Curvelet变换的对比 18

第三章 图像融合 19

3.1 图像融合 19

3.2 遥感图像融合 20

3.2.1 遥感图像融合背景 20

3.2.2 遥感图像融合的层次 21