The Application Of Low Rank Approximation In Image Compression

Images are important media to obtain, express and transmit messages, while they occupy a large amount of data space. It is very necessary that we compress the images because a large memory and bandwidth will be needed if they are stored and transmitted straight.This paper mainly focuses on the realization of image compression. And the maininnovation of this paper is SVGLRAM---a non-Iterative Algorithm of Generalized LowRank Approximations of Matrices and it will be proved theoretically and practically asfollows: Firstly, this paper reviews an important algorithm of Low RankApproximations of Matrices, that is, singular value approximation, its development,principle, and how to use the singular value decomposition to compress image, it has itsadvantage of the minimum error but the disadvantage of high time and space complexity.Secondly, this paper discusses another recently developed low rank approximationiterative algorithm of generalized low rank approximation. This algorithm can achievecompression of a number of images at one time, owning low time and space complexityas well; experiments are carried out to test its correctness in this part. Finally，this paperpresents SVGLRAM---a creative and non iterative algorithm. By selecting differentparameters from different face databases, the experimental results show that it can notonly obtain the error and the compression rate close to GLRAM, but also low time andspace complexity.