摘要：本次设计题目是基于主成分分析的图像压缩软件设计，课题主要意义是了解并且掌握主成分分析的原理和代码实现，研究图像压缩运用主成分算法的可行性并得出结论，主要目的是将主成分分析运用到图像压缩软件的设计中，实现对图像的批量压缩和解压功能。主成分分析（Principal components analysis，PCA）是一种分析、简化数据集的技术，它常用减少数据集的文数，同时保持数据集的对方差贡献最大的特征。这是通过保留低阶主成分，忽略高阶主成分做到的。在压缩过程中，压缩比的选择是一对矛盾，过大的压缩会使图像失真严重而失去意义，过小的压缩比对图像的压缩，传输，保存等意义不大，如何定性压缩图像的压缩比是决定这幅图像在压缩后是否细节能够得到足够保留的关键因素。5978
关键词：主成分分析（PCA）；文数；协方差矩阵；特征向量；特征值
Image compression software design based on principal component analysis
Abstract: The design subject image compression software design is based on principal component analysis, the main topic of significance to understand and master the principles of the principal component analysis and code, image compression using principal component algorithm feasibility and concluded, the main purpose is tothe principal component analysis is applied to the image compression software design, the bulk of the image compression and decompression functions. Principal component analysis (Principal Components Analysis, PCA) is an analysis, to simplify the technology of the dataset, it can be used to reduce the dimension of the data set, while maintaining the dataset each other differential is the greatest contribution characterized. This is done by retaining the low-level main component, and ignore the higher order principal component. During compression, the compression ratio selection is a contradiction, too much compression distort images lose their meaning, too small compressed image compression than the significance of image compression, transmission, preservation is not how qualitative the compression ratio of this image is determined whether the details can be obtained after compression is sufficient to retain the key factors.
Keywords: The principal component analysis（PCA）; dimension; covariance matrix; eigenvectors; eigenvalue
目录
摘要 i
Abstract ii
目录 iii
1 绪论 1
1.1 背景和意义 1
1.2 图像压缩技术的历史与现状 1
1.3 主成分分析及其在图象压缩软件设计中的应用 2
1.4 课题研究的主要内容 3
2 图像压缩的基本原理 4
2.1 图象压缩评价标准 4
2.2 主观标准 4
2.3 客观标准 5
2.4 图像压缩技术标准 5
2.5 图像压缩的分类 7
2.6 图像压缩处理技术基本理论 9
2.6.1 图像压缩的基本原理 9
2.6.2 图像压缩的基本模型 10
3 主成分分析基本原理及分析 11
3.1 数学定义 11
3.2 原理分析 12
3.3 算法详细过程 12
3.3.1 组织数据集 13
3.3.2 计算经验均值 13
3.3.3 计算平均偏差 13
3.3.4 求协方差矩阵 13
3.3.5 查找协方差矩阵的特征值和特征向量 13
3.3.6 特征值和特征向量的几何意义 14
4 MATLAB实现PCA图像压缩 16
4.1 MATLAB图像处理工具箱 16 基于主成分分析PCA图像压缩软件设计:http://www.751com.cn/jisuanji/lunwen_3267.html