Analysis of the Possibility of Using the Singular Value Decomposition in Image Compression

Abstract

In today’s highly computerized world, data compression is a key issue to minimize the costs associated with data storage and transfer. In 2019, more than 70% of the data sent over the network were images. This paper analyses the feasibility of using the SVD algorithm in image compression and shows that it improves the efficiency of JPEG and JPEG2000 compression. Image matrices were decomposed using the SVD algorithm before compression. It has also been shown that as the image dimensions increase, the fraction of eigenvalues that must be used to reconstruct the image in good quality decreases. The study was carried out on a large and diverse set of images, more than 2500 images were examined. The results were analyzed based on criteria typical for the evaluation of numerical algorithms operating on matrices and image compression: compression ratio, size of compressed file, MSE, number of bad pixels, complexity, numerical stability, easiness of implementation.