Research And Implementation Of PCA Face Image Compression And Reconstruction Algorithm

Principal component analysis method is developing rapidly in recent years, meanwhile used widely in many fields, and this paper focuses on the application of data dimensionality reduction. The image matrix is turned from two-dimensional matrix to one-dimensional vector, which is the foundation of PCA method, and then large dimensional covariance matrix is built to get eigenvalue and eigenvectors, so the PCA method is complex and costs a huge amount of computation. In recent years, by using two-dimensional Principal component analysis (2DPCA) and matrix Principal component analysis(MATPCA), time is saved and data dimensionality reduction is accomplished in different degrees.In this paper, based on PCA face image compression and reconstruction, lot of research is done on2DPCA, MATPCA facial image compression and reconstruction, so as to find an improved PCA method. This method is to make image training samples rows, columns equal divisions selectively, in order to obtain sub-images of the same size, and then a PCA analysis is done by collecting all the sub-set of training images together to get the corresponding overall covariance matrix. When the corresponding overall covariance matrixes are handled, the singular value decomposition is introduced to obtain eigenvalues and eigenvectors of the covariance matrix. Meanwhile when the test images are compressed, the test images are divided into sub-images exactly the way training images are processed, and they are compressed one by one; Then,the compressed images are rebuilt one by one to form the original images. My works in this paper are as follows:Firstly, a brief introduction on data dimensionality reduction’s purpose and significance is conducted, and a study on data dimensionality reduction is performed to summarize the common methods of data dimensionality reduction. This paper underlines the basic principles of principal component analysis algorithm.Secondly, the application from the data compression to facial image compression and reconstruction is presented. The PCA method needs two-dimensional images to be transferred into one-dimensional vectors. In order to avoid shortcomings of this method, by studying the2DPCA and MATPCA algorithm thought, these methods are compared and synthesized to get the improved algorithm. Finally, experiments are conducted to verify the related theoretical research, which contains two-dimensional data compression algorithms and reconstruction, image compression and reconstruction from two-dimensional data to simple images, meanwhile underlining the research on PCA,2DPCA, MATPCA and improved PCA on ORL face database, as well as compression and reconstruction of simple faces. The experiment shows the improved PCA has better robustness, and surpass other methods with excellent performance.