摘要由于成像设备以及成像过程中存在不可避免的造成图像质量退化因素，所以图像去噪和增强一直是图像学术领域和工程领域的重要研究内容。图像去噪和增强是利用计算机对图像进行平滑噪声，增强边缘等以满足更高层次的图像分析和理解。传统的去噪算法处理复杂图像时运行效率低，计算量大，无法较好的提高图像质量。而基于偏微分方程方法和变分法能够很好的克服上述问题，因此，有更好的应用前景。
本论文研究了三种不同的基于偏微分方程和变分法的去噪模型，分别是热传导方程，经典TV模型和无穷Laplace模型。通过数学理论分析和数值仿真实验，从定性和定量两个角度分别讨论了各模型的理论基础和去噪特点，最后通过去噪对比实验得出各模型的适用范围和优缺点。19405
关键词 图像去噪 热传导方程 TV模型 无穷拉普拉斯
毕业论文设计说明书（论文）外文摘要
Title The research of the digital image denoising and enhancement
Abstract
Because there are inevitable degeneration factors of image quality in the imaging equipment and imaging process ,so the image denoising and enhancement is always the important research content in academic field and engineering field. Image denoising and enhancement is to use the computer to smooth the image noise and enhancing edges, to meet the higher level of image analysis and understanding. When the traditional denoising algorithm deal with complex image,running efficiency is low and calculation is large ,which unable to improve the quality of the image. Based on partial differential equation method and the total variational method can overcome the above problems perfectly, therefore, has a better application prospect.
This paper studies the three different types of partial differential equations and total variational method based denoising model, the heat equation, the classic TV model and infinity Laplace model. Through mathematical theory analysis and numerical simulation, from the perspective of qualitative and quantitative discussed the theoretical basis of the model and characteristics of denoising respectively, finally through the denoising comparison experiment get the applicable range and advantages and disadvantages of each model.
Keywords: Image denoising, heat equation , TV model, infinity Laplace
目 次
1 绪论 1
1.1 研究背景和意义 1
1.2 数字图像处理基础 1
1.3 研究历史与现状 4
1.4 本文的主要工作和结构 5
2 人眼视觉成像原理 6
2.1 视觉的形成 6
2.2 视觉系统的特性 6
2.3 视觉掩盖效应 7
3 基于热传导方程的图像去噪 9
3.1 基本理论分析 9
3.2 用热传导方程去噪的仿真分析 11
3.3 高斯平滑滤波器 13
3.4 本章小结 15
4 基于TV模型的图像去噪 17
4.1 经典TV去噪模型分析 17
4.2 不同正则项范数的去噪模型 21
4.3 本章小结 22
5 基于无限拉普拉斯的图像分解 23
5.1 图像分解模型的发展 23
5.2 利用无穷LAPLACE进行图像分解的新模型 25
5.3 本章小结 29
6 去噪结果对比分析 30
结论 33
致谢 34 数字图像的去噪与增强研究:http://www.751com.cn/shuxue/lunwen_10747.html