ZDH131-09-郑子道.docx

《数字图像处理》项目设计报告——基于PCA的图像压缩与重建学 院：电气工程与自动化专业班级： 自动化131学号：2420132899、09学生姓名： 郑子道指导老师： 杨国亮时 间：2016.11.21AbstractPrincipal component analysis has developed rapidly in recent years, the field of its application is also more and more widely. In this paper, we mainly use it to reduce the dimension of data. Because the PCA method needs to transform the image matrix from the two-dimensional matrix into one dimensional vector, the covariance matrix of the dimension is constructed, and the characteristic value and the characteristic vector are solved. Two dimensional principal component analysis (2DPCA) and matrix principal component analysis (MATPCA) have been made in recent years, which have different degrees of improvement in the computation time and data dimension. In this paper, based on the PCA face image compression and reconstruction method based on the research, 2DPCA and MATPCA face image compression and reconstruction method, and on the basis of the implementation of an improved PCA method, namely the training sample image can be selected row and column equal division, some are the same size of the sub image then, all the sub images of training images set in PCA analysis, get the corresponding covariance matrices. In dealing with the total covariance matrix, the singular value decomposition is introduced to solve the eigenvalues and eigenvectors of the covariance matrix. Also in the compression of the test image, the image division method in advance in accordance with the training that will test the image into sub images, and then on the image compression and reconstruction is by reconstruction of the compressed sub image, and then spliced into the original image.Keywords：PCA；Data Reduction；Robustness；Compress；Reconstruction摘要主成分分析近年来发展比较迅速,其应用的领域也越来越广泛,在本文中主要借助于其对数据降维的应用。由于PCA方法需要将图像矩阵由二维矩阵转化成一维向量,构造出维数比较庞大的协方差矩阵,在此基础上求解特征值和特征向量,计算量巨大而且复杂。近年来也出现了二维主成分分析(2DPCA)和矩阵主成分分析(MATPCA),在计算时间和数据降维方面均有不同程度的提高。 本文在基于PCA图像压缩与重建方法基础上,研究了2DPCA、MATPCA图像压缩与重建方法,并在此基础上了实现了一种改进的