华侨大学厦门工学院 毕业设计（论文）
结论
本文通过对小波变换的研究，介绍了小波变换技术在国内外的发展概况，阐述了其基本理论及其在图像处理方面的应用，包括了小波变换的基本概念、特征、分类。简单介绍了从传统傅立叶变换到小波变换的技术发展，体现小波变换在图像处理上的优越性。使用MATLAB编程的方法实现小波变换在图像压缩、图像增强、图像去噪、图像融合、图像分解和图像重构的算法，说明了小波变换在图像处理方面的重要性。简单扼要地介绍了一些处理图像的关键小波函数的调用方法，体现运用小波变换对算法的简化效果十分明显。为了验证本文算法可行性，对其进行了仿真实验，并把整个实验的算法做成了人机交互界面（GUI）,直观、方便。
本文算法相对较为简单明了，虽然有待进一步对小波变换理论深入研究，但却已然表现了小波变换和传统变换相比的优越性，同时体现了小波变换已经可以广泛应用在图像处理领域中，并占据重要作用，拥有广大的发展前景。
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小波变换在图像处理中的应用
参考文献
[1] 张德丰.详解MATLAB数字图像处理，电子工业出版社，2010 [2] 刘刚.王立香，董延，MATLAB数字图像处理，机械工业出版社，2010 [3] 郑阿奇，曹戈.MATLAB实用教程（第3版）.北京：电子工业出版社，2012 [4] 董长虹，高志等.MATLAB小波分析工具箱原理与应用.北京：国防工业出版社，2004 [5] 赵小川等.MATLAB数字图像处理实战，机械工业出版社，2013 [6] 张汗灵.MATLAB在图像处理中的应用，清华大学出版社，2008 [7] 刘贵忠，邸双亮.小波分析及其应用.西安电子科技大学出版社，1992 [8] 成礼智，王红霞，罗永.小波的理论与应用.北京：科学出版社，2004 [9] 成礼智，郭汉伟.小波与离散变换理论及工程实践〔M].清华大学出版社，2005 [10] 赵书兰.MATLAB R2008 数字图像处理与分析实例教程.北京:化学工业出版社，2009.6
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华侨大学厦门工学院 毕业设计（论文）
致 谢
时光匆匆，美好的四年大学生活转瞬即过。在本文完成之际，衷心感谢我的指导老师杨艺敏老师的教导和帮助。杨老师用渊博的专业知识，严谨的治学态度在毕业设计和毕业论文的完成过程中给予了耐心的指导和督促，在我遇到程序算法问题及论文问题的时候，细心给我指出问题的错误点，并提供了许多的参考建议和改善方向，杨老师精益求精的工作作风对我毕业后的工作生活树立了一个良好的榜样。
最后，感谢我的母校的传道、授业、解惑。感谢所有在大学给我过教育指导的老师对我的精心栽培。感谢所有在大学四年互帮互助的同学，让我在阳光和笑容中收获珍贵的友谊和宝贵的知识。
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小波变换在图像处理中的应用
附录 英文文献及翻译
MATLAB wavelet analysis and image compression
Abstract
Wavelets provide a powerful and remarkably flexible set of tools for handling fundamental problems in science and engineering, such as audio de-noising, signal compression, object detection and fingerprint compression, image de-noising, image enhancement, image recognition, diagnostic heart trouble and speech recognition, to name a few. Here, we are going to concentrate on wavelet application in the field of Image Compression so as to observe how wavelet is implemented to be applied to an image in the process of compression, and also how mathematical aspects of wavelet affect the compression process and the results of it. Wavelet image compression is performed with various known wavelets with different mathematical properties. We study the insights of how wavelets in mathematics are implemented in a way to fit the engineering model of image compression. 1. Introduction
Wavelets are functions which allow data analysis of signals or images, according to scales or resolutions. The processing of signals by wavelet algorithms in factworks much the same way the human eye does; or the way a digital camera processes visual scales of resolutions, and intermediate details. But the same principle also captures cell phone signals, and even digitized color images used in medicine.Wavelets are of real use in these areas, for example in approximating data with sharp discontinuities such as choppy signals, or pictures with lots of edges.
While wavelets is perhaps a chapter in function theory, we show that the algorithms that result are key to the processing of numbers, or more precisely of digitized information, signals, time series, movies, color images, etc. Thus, applications of the wavelet idea include big parts of signal and image pro-cessing, data compression, fingerprint encoding, and many other fields of science and engineering. This thesis focuses on the processing of color images with the use of custom designed wavelet algorithms, and mathematical threshold filters.
Although there have been a number of recent papers on the operator theory of wavelets, there is a need for a tutorial which explains some applied tends from scratch to operator theorists. Wavelets as a subject is highly interdisciplinary and it draws in crucial ways on ideas from the outside world. We aim to outline various connections between Hilbert space geometry and image processing. Thus, we hope to help students and researchers from one area understand what is going on in the other. One difficulty with communicating across areas is a vast difference in
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华侨大学厦门工学院 毕业设计（论文）
lingo,jargon, and mathematical terminology.
With hands-on experiments, our paper is meant to help create a better understanding of links between the two sides, math and images. It is a delicate balance deciding what to include. In choosing, we had in mind students in operator theory,stressing explanations that are not easy to find in the journal literature.
Our paper results extend what was previously known, and we hope yields new insight into scaling and of representation of color images; especially, we have aimed for better algorithms. The paper concludes with a set of computer generated images which serve to illustrate our ideas and our algorithms, and also with the resulting compressed images. 1.1. Overview.
Wavelet Image Processing enables computers to store an image in many scales of resolutions, thus decomposing an image into various levels and types of details and approximation with different valued resolutions. Hence, making it possible to zoom in to obtain more detail of the trees, leaves and even a monkey on top of the tree. Wavelets allow one to compress the image using less storage space with more details of the image.The advantage of decomposing images to approximate and detail parts as in 3.3 is that it enables to isolate and manipulate the data with specific properties. With this, it is possible to determine whether to preserve more specific details. For instance, keeping more vertical detail instead of keeping all the horizontal, diagonal and vertical details of an image that has more vertical aspects. This would allowthe image to lose a certain amount of horizontal and diagonal details, but would not affect the image in human perception.
As mathematically illustrated in 3.3, an image can be decomposed into approximate, horizontal, vertical and diagonal details. N levels of decomposition is done. After that, quantization is done on the decomposed image where different quantization maybe done on different components thus maximizing the amount of needed details and ignoring ?not-so-wanted? details. This is done by thresholding where some coefficient values for pixels in images are ?thrown out? or set to zero or some ?smoothing? effect is done on the image matrix. This process is used in JPEG2000. 1.2. Motivation.
In many papers and books, the topics in wavelets and image processing are discussed in mostly in one extreme, namely in terms of engineering aspects of it or wavelets are discussed in terms operators without being specifically mentioned how it is being used in its application in engineering. In this paper, the author adds onto [Sko01], [Use01] and [Vet01] more insights about mathematical properties such as properties from Operator Theory, Functional Analysis, etc. of wavelets playing a major role in results in wavelet image compression. Our paper aims in
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