Application of singular value decomposition and non-negative matrix factorization in image compression.

摘要

Matrix factorization or matrix decomposition is defined by factorizing a matrix into a product of some matrices. There are different types of matrix decompositions: LU decompositions, non-negative matrix factorization (NMF), singular value decomposition (SVD) etc. Any image can be represented as a matrix. Each matrix element is an intensity value of a pixel. The matrix from the image usually has high dimension. SVD and NMF useful to reduce the dimensionality of the data. Using SVD, some singular values from singular matrix has been removed. Then we get the approximation of the original matrix. On the other hand, NMF consists of reduced rank non-negative factors (two non-negative matrices). The approximation matrix gives the new compressed image.;In this study we compressed two images (Cleve Morel, Designer of MATLAB, and a Cat) of sizes 720 by 1280 and 400 by 363 pixels respectively using MATLAB. We also made a comparison between the performances of SVD and NMF in image compression. Key Words: