Image Compression Using Singular Value Decomposition

We can utilize Singular Value Decomposition (SVD) technology to compress images. SVD is a mathematical technique that decomposes a matrix into three constituent matrices, enabling effective image compression. In the experimental documentation, we provide comprehensive details about the programming approach and implementation process of SVD, featuring key functions such as svd() for matrix decomposition and rank approximation algorithms. The implementation typically involves converting RGB images to grayscale matrices, applying SVD decomposition, and reconstructing images using reduced-rank approximations by retaining only the most significant singular values and vectors. We conduct thorough analysis of experimental results comparing compression ratios and image quality metrics like PSNR (Peak Signal-to-Noise Ratio). Additionally, we include sample images used in the experiments to better demonstrate the practical application of SVD in image compression, showcasing how varying the number of retained singular values affects both compression efficiency and visual quality.