Digital Image Compression Based on Singular Value Decomposition Algorithm

Abstract

Image compression represents a fundamental application of data compression techniques within the field of digital image processing. As digital images contain vast amounts of information, there is a critical need for efficien t methods to store and transmit large data volumes. This research explores the Singular Value Decomposition (SVD) algorithm as a robust mathematical framework for achieving image compression by leveraging low-rank matrix approximations. The primary objective is to implement the SVD algorithm and evaluate its performance based on specific metrics, namely Peak Signal-to-Noise Ratio (PSNR) and Mean Square Error (MSE). The study provides a detailed investigation into the trade-off between the compression ratio and the resulting image quality. Methodologically, the SVD process factorizes an image matrix A into three distinct components: U, S, and V^T. By retaining only, the first r singular values—which contain the maximum signal energy—the algorithm can effectively reconstruct an approximation of the original image using significantly less storage space. Experimental simulations were conducted using MATLAB on various test images, including grayscale (such as Lena and Baboon) and full-color RGB images. Results demonstrate that image clarity improves as more singular values are reintroduced. For a 256 * 256 grayscale image, a close resemblance to the original was achieved using only 90 singular values, yielding a PSNR of 37.42 dB. In color images, the process involves decomposing the red, green, and blue saturation matrices separately before recombination. The findings confirm that while higher rank values increase image fidelity, they simultaneously reduce the compression ratio. Ultimately, SVD is shown to be a stable and effective numerical method for splitting data into signal and noise subspaces, providing a practical solution for modern digital communication requirements.