Computational analysis of adaptive Singular Value Decomposition algorithm to 2D and 3D still image compression application

Abstract

Data/image compression is a significant application of linear algebra. The need to minimize the amount of digital information stored and transmitted is an ever growing concern in the modern world. Singular Value Decomposition (SVD) is an effective tool for minimizing data storage and data transfer. The proposed work explores image compression through the use of SVD on image matrices. The performance analysis of such an algorithm is measured in terms of Peak Signal to Noise Ratio (PSNR), Compression Ratio (CR), Mean Square Error (MSE) for 2-Dimensional and 3-Dimensional still images by varying the rank of image matrix (k). The maximum rank of image matrix considered is 150, allows fair reproduction of images with high PSNR and lower MSE. For diverse applications, the method analyzed here provides a good alternative to the existing algorithms by adapting different rank of matrices.